Frequency Chirping Properties of Electroabsorption

Frequency Chirping Properties of

Electroabsorption Modulators

Integrated with Laser Diodes

UN

IVERSI TÄ T

ULM·

SC

IEN

DO

·DOCENDO·C

UR

AN

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·

Dissertation

zur Erlangung des akademischen Grades eines

Doktor-Ingenieurs (Dr.-Ing.)

der Fakultat fur Ingenieurwissenschaften

der Universitat Ulm

von

Brem Kumar Saravanan

aus Mayiladuthurai (Indien)

1. Gutachter: Prof. Dr.rer.nat. K. J. Ebeling

2. Gutachter: Prof. Dr.rer.nat. habil. H. Hillmer

Amtierender Dekan: Prof. Dr.-Ing. H.-J. Pfleiderer

Datum der Promotion: 10 Apr 2006

2006

In memory of Bernhard Stegmuller

Acknowledgments

It has been my pleasure to conduct my work at Corporate Research Technology Labs (for-

merly Corporate Research Photonics). The work described in this thesis would not have

been possible without the help of my coworkers and comrades in the Photonics group.

In this respect, I am grateful to Bernhard Stegmueller for originally motivating this project,

and supporting my work in this direction. He provided many valuable insights into the in-

trinsic device physics and was always willing to take the time to explain things to me. It

was unfortunate to experience his sudden demise during the course of my work. More than

any other person that I know, Christian Hanke has fostered my independence while at the

same time remaining approachable and encouraging. Since the inception of this project, he

has been a source of encouragement and enlightenment. I must also thank him for his time

in helping me out of the practical difficulties while building my measurement setup.

Martin Peschke has been a great source of suggestions and speculations, from device design

to high-speed performance. I am thankful for his careful reading of this thesis and his valu-

able criticisms. Thomas Wenger and Roberto Macaluso have been very generous in helping

me get the devices from the fabrication lab to my measurement setup in time. I thank Har-

ald Hedrich for assisting me with the automation of the measurement setup and Reinhard

Maerz for his generosity in allowing me to use his signal processing environment. I am grate-

ful to Henning Riechert for his constant source of encouragement throughout my thesis work.

I have no doubt that much of the success of this work can be attributed to these talented and

dedicated individuals that I have had the opportunity to work with over the past three years.

Beyond my colleagues in the Photonics group, there are several other members who have

contributed to this project considerably. Most notably, Josef Rieger for growing the epitaxial

structures and Jorg Adler for performing the grating technology, Christian Degen and Marc

Ilzhofer in lending me with optics accessories all from the Fiber Optics group. I acknowledge

Martin Wurzer and Herbert Knapp from the High Frequency group for helping me out with

some high frequency components.

There are also non-localized sources who have been of considerable importance to this work.

Philipp Gerlach for his valuable discussions, and Rainer Michalzik from the University of

Ulm deserve special thanks in this respect.

I feel it necessary to mention also the friends who have been with me in the past few years.

Although they have perhaps not contributed directly to this work, their support and encour-

agement outside of my research is part of what kept me going those times when research

wasn’t going as well as I. In particular, I would like to thank Arun Ramakrishnan for his

v

irresistible support and encouragement during the last three years. My erstwhile college

mates Kishore Kumar Sathyanandam, Muralidharan Balakrishnan, Bijoy Rajasekharan and

my Matlab companion Nilesh Madhu deserve special thanks for their support, suggestions

and discussions.

Thanks are due to my parents and my family for their constant support over the years. The

encouragement and love that they have selflessly and tirelessly invested in me is undoubtedly

the greatest source of my ambition, inspiration, dedication and motivation.

I gratefully acknowledge the financial support provided by “Bundesministerium fur Bildung

und Forschung” (the German Federal Ministry of Education and Research) during my thesis

work at Infineon.

My sincere thanks are due to Prof. Dr. Hartmut Hillmer, University of Kassel for cheerfully

agreeing to act as second referee and for his cooperation, comments and suggestions during

the final phase of this work.

Last but not least, I would like to thank my supervisor Prof. Dr. Karl Joachim Ebeling,

President, University of Ulm, who trusted me handle this project and giving me an oppor-

tunity to work under his expert mentorship.

You have all helped me out, often without even knowing it, and I hope I can reciprocate.

vi

Contents

1 Introduction 1

2 Device Principle 6

2.1 Principle of operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Epitaxial layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Device fabrication and layout . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Theory 11

3.1 Field induced absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2 Optical gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.3 Optical waveguiding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.4 Material system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.5 Distributed feedback lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.6 Electroabsorption modulators . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.7 Semiconductor optical amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.8 Frequency chirp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.9 Dynamic frequency modulation performance . . . . . . . . . . . . . . . . . . 29

3.10 Phase modulation in semiconductor optical amplifiers . . . . . . . . . . . . . 35

3.11 Optical fiber dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.12 Noise in optical detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4 Characterizing Frequency Modulation (FM) Properties 42

4.1 Chirp-parameter extraction from photocurrent absorption measurements . . 44

4.2 Small-signal chirp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.2.1 Principle of measurement . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.2.2 Experimental setup for small-signal chirp measurements . . . . . . . 51

4.3 Time-resolved chirp (TRC) measurements . . . . . . . . . . . . . . . . . . . 52

4.3.1 Principle of measurement . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.3.2 Design of Fabry-Perot resonator . . . . . . . . . . . . . . . . . . . . . 56

4.3.3 Experimental setup for TRC measurements . . . . . . . . . . . . . . 59

4.3.4 Phase distortion in Fabry-Perot resonators . . . . . . . . . . . . . . . 62

4.3.5 TRC measurement considerations . . . . . . . . . . . . . . . . . . . . 67

vii

4.3.6 Estimation of effective chirp-parameter . . . . . . . . . . . . . . . . . 69

4.4 Impact of chirp on system performance . . . . . . . . . . . . . . . . . . . . . 70

5 Experimental Setup for Dynamic Characterization 72

5.1 Large-signal characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.2 Time-resolved chirp characterization . . . . . . . . . . . . . . . . . . . . . . 72

6 1310 nm Electroabsorption Modulated Lasers 76

6.1 Static characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

6.2 Electrical characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

6.3 Dynamic intensity modulation response . . . . . . . . . . . . . . . . . . . . . 81

6.3.1 Small-signal response . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

6.3.2 Large-signal modulation results . . . . . . . . . . . . . . . . . . . . . 83

6.4 Dynamic frequency modulation response . . . . . . . . . . . . . . . . . . . . 84

6.4.1 Small-signal chirp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

6.4.2 Time-resolved chirp . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

7 1550 nm Electroabsorption Modulated Lasers 89





7.3 Semi-cooled electroabsorption modulated lasers . . . . . . . . . . . . . . . . 98


8 1550 nm Electroabsorption Modulated Lasers Integrated with SOAs 104






9 Conclusions 110

A Device Layer Structure 115

B Kramers-Kronig Relations 117

C Frequency Domain Analysis 120

D List of Symbols 122

viii

E List of Acronyms 128

List of Publications 131

References 133

Curriculum Vitae 139

ix

Chapter 1

Introduction

The advent of low loss optical fibers in the eighties and the subsequent development of efficient

and inexpensive quantum well laser sources during the early nineties has had tremendous

impact on the telecommunication industry. Today, semiconductor laser sources form the key

building blocks of optical communication networks.

The optical telecommunication industry primarily exploits two wavelength windows for single-

mode applications, namely, 1310 nm and 1550 nm. Two fundamental standards defined by

the international telecommunication union (ITU) to address the telecommunication industry

are synchronous optical networks (SONET) and synchronous digital hierarchy (SDH). The

two bodies, SONET and SDH, work in close cooperation and hence in most respects the two

standards are functionally equivalent. Depending on the link distance, SONET classification

of optical networks fall under one of the following categories:

(a) short reach (SR) intended for very short interconnect distances, typically less than 2 km.

(b) intermediate reach (IR) applications intended for distances up to 15 km.

(c) long reach (LR) up to 40 km and 80 km for 1310 nm and 1550 nm wavelength windows,

respectively.

One of the prime concerns in the design and deployment of optical transmitters for the differ-

ent link distances mentioned above is the chirping behavior of the transmitter. The chirping

behavior is characterized by the linewidth enhancement factor (LEF) earlier introduced by

Henry [1] for characterizing chirp induced spectral broadening of semiconductor laser sources.

More generally, the parameter came to be known as Henry-parameter or chirp-parameter de-

noted by ‘αH’. The chirp-parameter αH, is a figure of merit to compare the performance of

different transmitters. It basically describes the extent of frequency deviations encountered

with respect to the unmodulated laser carrier frequency for a given light extinction under

large-signal modulation conditions. Such frequency excursions in the time domain inevitably

broaden the frequency spectrum of a pulse. Such a pulse encompassing a range of frequencies

is susceptible to chromatic dispersion effects in optical fibers [2], i.e., different frequency com-

ponents propagate with different group velocities leading to pulse distortion in time domain.

1

2 Chapter 1. Introduction

Standard single-mode fibers (SSMFs) feature a dispersion minimum, with the zero dispersion

wavelength occurring near 1300 nm. Hence frequency chirping is not critical in the 1310 nm

wavelength window. However, fiber attenuation values assume 0.5 decibels/kilometer (ab-

breviated as 0.5 dB/km), which renders this window primarily loss-limited.

The 1550 nm wavelength window features a loss minimum of 0.2 dB/km. Further, the avail-

ability of erbium-doped fiber amplifiers (EDFAs) thrives the constant progress in the de-

ployment of transmitters emitting in the 1550 nm wavelength window. However, the major

impairment here is due to the dispersion coefficient of the optical fiber with values around

+17 ps/(nm·km). Thus, a chirped pulse suffers severe pulse distortion which renders this

window primarily dispersion-limited.

As of today, for single-mode applications, directly modulated distributed feedback lasers

(DFB) have been commercially deployed up to 2.5 Gigabit per second (Gbps). In such direct

modulation applications, the laser current is modulated to encode message onto the laser

carrier frequency (peak emission frequency of laser). This inevitably results in change of

carrier frequency due to relaxation oscillations in the carrier density [3, 4]. The result is a

phase modulation of the carrier frequency due to the associated real refractive index changes

of the active region. Consequently, for data rates exceeding 10 Gbps severe frequency chirping

results.

Typical αH values of directly modulated semiconductor lasers1 have been reported between

2 and 7 [1, 3, 5–7]. This is not a critical issue for short reach applications (e.g. enterprise

networks), but could be a serious limiting factor for intermediate and long reach applications.

Thus, besides other factors such as fiber attenuation and nonlinearities, dispersion limits the

maximum transmission distance that can be obtained for a given bit rate and a specified bit

error rate (BER) performance.

In order to overcome the chirp induced limitations of directly modulated lasers (DMLs) and

simultaneously achieve data rates in excess of 10 Gbps, external modulation of light has been

widely studied [8, 9], and henceforth implemented. In the case of external modulation, the

functionalities of light generation and modulation are accomplished by different devices. The

laser diode is operated in a continuous wave (CW) mode, and the optical wave is externally

modulated by an optical modulator.

Within the context of monolithic integration, integration of electroabsorption modulators

(EAMs) with DFB lasers (the integrated device is also referred to as electroabsorption mod-

1In this work, the sign of chirp-parameter (αH) values of directly modulated semiconductor lasers isdefined as ‘positive’. Some authors prefer to define them as ‘negative’. This is only a matter of conventionand the actual frequency chirping properties remain identical. However, a comparison of chirp-parametervalues reported by different authors (or a comparison with external modulators) is justified only if consistent

expressions were used while defining the sign of the chirp-parameter and the large-signal dynamic extinction

ratio is explicitly specified at the operating wavelength.

3

ulated lasers; abbreviated as EMLs) have been extensively studied [10–14] for intensity mo-

dulation (IM) schemes. In such EAMs, modulation is achieved by way of a bias controlled

absorption coefficient of a waveguide structure. Depending on the active layer used, they can

be further classified into two types: EAMs employing a bulk active layer which is based on

the Franz-Keldysh effect [15,16] and EAMs employing quantum wells. The electroabsorption

effect in the latter is much more pronounced and is referred to as the quantum confined Stark

effect (QCSE) [17–19]. One of the prime motivations for the continuous progress of QCSE

based EAMs can be attributed to the low chirping behavior [20] as compared to directly

modulated counterparts. For instance, typical magnitudes of αH values lie in the range of

0–1 [19,21]. Besides low chirping, well designed QCSE based EAMs allow for device lengths

in the range of 75–150µm achieving high-speed operation without compromising extinction

ratios [22]. Other salient features include low drive voltage swings, typically 1–3 V [23–25]

and compact realization of the devices with small footprints [26] which considerably reduces

packaging costs.

Specifically, this thesis explores the potential of EMLs for systems employing direct detection

of non-return to zero (NRZ) signals for intermediate and long reach applications (i.e., up to

80 km). EMLs emitting in the 1310 nm and 1550 nm wavelength windows have been employed

for the investigations. The EMLs exploit a shared active area (i.e., active area employed is

identical) for the laser and the modulator sections based on the promising InGaAlAs/InP

material system [27]. Shared active area EMLs reduce the fabrication complexity consider-

ably and are promising candidates for cost-effective solutions.

In order to reliably estimate the transmission capability of the fabricated EMLs, a knowl-

edge of the dynamic chirping behavior is of paramount importance. This is essential to

both assess the performance of an optical communication system and optimize it to enhance

the distance-bandwidth product. The optimization can include both the optimization of the

chirping properties of the transmitter and the total dispersion of the transmission link by way

of dispersion management [28]. Motivated by the aforementioned arguments, the primary

goal of this work is to design and demonstrate a time-resolved chirp (TRC) measurement

setup for characterizing the dynamic chirping behavior of high-speed EMLs, i.e., EMLs ca-

pable of operating at data rates above 10 Gbps.

Before performing time-resolved chirp (TRC) measurements, the devices are investigated

under static and dynamic conditions. This facilitates a comprehensive understanding of the

device properties and further deduction of optimum operation points. This includes, for

instance, the investigation of small-signal electro-optic (E/O) behavior of the devices.

Up to some extent, negative chirp transmitters can be exploited to compensate the positive

dispersion coefficient of the fiber [29,30]. Hence, the quest for negative chirp transmitters is a

direct consequence of extending the transmission distance in the 1550 nm wavelength window

for a specific bit rate. However, Kramers-Kronig transformations of EML absorption charac-

4 Chapter 1. Introduction

teristics show that negative chirp-parameters can be achieved only for very low optical power

levels. Although hybrid EML approaches enable high optical power levels by way of indepen-

dent optimization of the active layer (of the laser and modulator sections), they still suffer

from positive frequency chirping due to the inherent larger wavelength detuning. In order

to keep the fabrication complexity as simple as possible and simultaneously accomplish high

optical power and negative chirp-parameters, the possibility of integrating a semiconductor

optical amplifier (SOA) will be explored. SOAs not only boost the optical power [31] but,

under gain saturation conditions, compensate for the positive chirp of an electroabsorption

modulator. The feasibility of enabling very low or negative chirp-parameters with an SOA

forms an additional motivation of this work.

Uncooled EMLs, i.e., EMLs operating without an active temperature control over a tem-

perature range of 0–85C, emitting in the 1310 nm wavelength window have been demon-

strated [32] at 10 Gbps and are commercially available on the market today [33]. Such un-

cooled EML approaches reduce on-chip power consumption, thereby adding further potential

to the existing data communication market. The seek for such temperature independent op-

eration of EMLs by way of temperature dependent static and high-speed measurements is

also addressed in this work.

The thesis is organized as follows:

Chapter 2 introduces the epitaxial layer structure of the integrated device. Basic principles

of device operation are described in a qualitative manner. Finally, a general layout of a

fabricated EML integrated with an SOA is outlined.

Chapter 3 reviews the theoretical framework behind the operation of the devices. It starts

with a brief description of absorption and gain mechanisms and proceeds to device specific

properties such as insertion loss and extinction behavior. Subsequently, the EAM is modeled

as a combination of an intensity and a phase modulator and an expression for the chirp-

parameter is presented. The effect of wavelength detuning on the sign and magnitude of the

chirp-parameter is discussed.

Chapter 4 describes the different measurement tools invoked for characterizing chirp. This

includes the Kramers-Kronig transformations used as a starting point to analyze the chirp

behavior of the devices. Secondly, chirp-parameter extraction under small-signal modulation

conditions is described. In the later part of the chapter, the principle of time-resolved chirp

measurements using the transmission characteristics of an interferometer is outlined. Subse-

quently, the time-resolved chirp measurement setup implemented using an air-cavity based

Fabry-Perot resonator is presented. Finally, the measurement considerations for high-speed

time-resolved chirp measurements are summarized.

Chapter 5 outlines the experimental setup that is used for most of the static, dynamic inten-

5

sity modulation and time-resolved chirp measurements performed in this work. The validity

of the realized time-resolved chirp measurement setup is tested using a commercial Mach-

Zehnder modulator.

Chapter 6 and Chapter 7 present the experimental results of EMLs emitting in the 1310 nm

and 1550 nm wavelength windows, respectively. The experimental results on semi-cooled op-

eration of EMLs in the 1550 nm wavelength window are included in Chapter 7. Chapter 8 is

devoted to EMLs integrated with SOAs emitting in the 1550 nm wavelength window. Finally,

the results are concluded in Chapter 9.

The corresponding layer structures of EMLs emitting in the 1310 nm and 1550 nm wavelength

windows are provided in Appendix A. A derivation of the “Kramers-Kronig” relations can

be found in Appendix B. A concise introduction to frequency domain analysis of signals and

its application to this work is presented in Appendix C.

Chapter 2

Device Principle

This chapter introduces the principle of operation of the integrated device. The corresponding

epitaxial layer structure is outlined subsequently. A brief description of the fabrication steps

involved and a schematic of the device layout after complete fabrication is presented in the

final part of this chapter.

2.1 Principle of operation

The integrated device consists of a distributed feedback laser diode and an electroabsorption

modulator fabricated on a single substrate. The term “electroabsorption modulated lasers”

(EMLs), as it is popularly referred to in the literature, shall be used henceforth to refer to

the device.

Wavelength selectionand amplification

intrinsic MQWactive layer

DFB Laser

Amplification

EAM SOA (optional)

Modulation

p-doped

n-doped

Forward bias Forward biasReverse bias

grating

direction oflight output

Fig. 2.1: Schematic illustration of a monolithically integrated distributed feedback laser, electroab-sorption modulator and a semiconductor optical amplifier.

In the 1550 nm wavelength window, EMLs integrated with semiconductor optical amplifiers

are also studied. The latter combination shall be referred to as EML-SOAs.

6

2.1. Principle of operation 7

Laser and SOA sections

In the laser section, the p-i-n structure is forward biased. For external voltages approximately

equal to E21/q, where E21 and q represent the transition energy at equilibrium and electron

elementary charge respectively, the potential energy barrier between the n- and p-regions is

lifted (for the case of highly doped degenerate semiconductors under consideration). Thus a

flat band condition is established with the carrier distributions in the conduction band (CB)

and valence band (VB) described by the quasi-Fermi levels. For external voltages greater

than E21/q, carrier inversion is established by electron and hole injection from the n- and

p-doped regions into the quantum wells, respectively. This carrier inversion forms the basic

mechanism behind the gain process [6] as sketched in Fig. 2.2 (lower half). In the case of

an optional SOA section, the SOA is operated under forward bias conditions similar to the

laser section.

EAM section

Typical absorption spectra of an EAM employing a multiple quantum well (MQW) active

layer is shown schematically in Fig. 2.2 (upper half).

Ab

sorp

tio

nG

ain

0V

-1V

+1V

Forwardbiased

Reversebiased

EAM

Laser/SOA

Operatingwavelength

MQWactive layer

p n

__

+

Ec

Ev

p n

Ec

Ev

__

+

p

n

Wavelength

Fig. 2.2: Schematic of gain and absorption spectra of the active quantum well material for laserand modulator sections, respectively. Typical shift of the absorption curve for a reverse bias inthe EAM section is shown. The DFB wavelength of operation is also indicated. A sketch of thecorresponding band diagrams is shown on the right-hand side.

8 Chapter 2. Device Principle

The absorption spectra are shown for two different bias voltages 0 V and −1 V. Upon ap-

plication of −1 V on the EAM, the energy bands tilt with respect to the built-in field band

profile at 0 V as sketched in the band diagram representation. This results in a reduction

of the separation of the energy states in the quantum wells. Thus absorption of photons

slightly less than that of the unbiased case becomes feasible. This effect is termed as the

quantum confined Stark effect (QCSE) [3]. The QCSE effect manifests itself as a shift of the

absorption edge toward longer wavelengths in the EAM absorption spectra.

For an optimum device performance, the wavelength of operation has to guarantee low in-

sertion losses and high absorption swings in the EAM section. In the case of laser or SOA

sections, sufficient gain at the operating wavelength is needed to obtain moderate thresh-

old currents and amplification. In general, an application dependent compromise has to be

found in defining the operating wavelength, counter balancing the trade-off between absorp-

tion swing and gain [34].

2.2 Epitaxial layout

There are two epitaxial growth steps involved in the fabrication of the device.

The first step comprises the growth of the multiple quantum well active layer and the grating

layer. The growth process is performed by low-pressure metal organic vapor phase epitaxy

(MOVPE) on a (100) oriented semi-insulating (s.i.) InP substrate. The semi-insulating

substrate is used for improving the high frequency performance of the fabricated devices.

The intrinsic active layer consists of InGaAlAs quantum wells (10 to 11 in number, cf. Ap-

pendix A), embedded in a separate confinement heterostructure (SCH). The dimensions of

the individual layers are highly exaggerated for illustration purposes in Fig. 2.3. The nom-

inally undoped SCH layers positioned on the top and bottom of the multiple quantum well

structure enable both carrier and optical field confinement [34]. Subsequently, the operating

wavelength in the DFB section is defined by a holographic grating process followed by wet-

chemical etching.

In the following second epitaxial step, the grating layer is overgrown by a 1.6µm thick InP

ridge layer and a 200 nm thick ternary InGaAs p++−contact layer [13]. Fig. 2.3 shows a

schematic layer structure of the EML after the overgrowth process illustrating the exploita-

tion of an identical multiple quantum well active layer in both the laser and modulator

sections.

Electrical isolation between the laser and EAM sections is achieved by etching a trench in

the p-doped cladding region as indicated in Fig. 2.3. Typical measured values of electrical

isolation lie in the range of 45 kΩ. For the case of an SOA integrated with an EML, the SOA

shares the identical active layer as that of laser and modulator sections.

2.3. Device fabrication and layout 9

direction oflight output

InGaAlAs QWsfor lasing &modulation

SCH

grating

SCH

DFB Laser EAMp-typecontact

p-doped p-doped

+ -

p++

electrical

n-typecontactsemi-insulating substrate

n-dopedn++

isolation

Fig. 2.3: Schematic layer structure of theintegrated DFB laser and electroabsorptionmodulator. The identical active layer con-sists of InGaAlAs quantum wells. Holograph-ically defined grating achieves wavelength se-lectivity in the laser section. Separate confine-ment heterostructures (SCHs) confine light inthe transversal direction. An etched trenchprovides electrical isolation between the twosections.

2.3 Device fabrication and layout

The ridge waveguide structures with typical widths of 2µm are defined by depositing the p-

type contact stripes, using lift-off technique, and a subsequent standard dry and wet-chemical

etching.

In the following dry etching step, a second mesa of 20µm and 2.2µm width in the laser

(and SOA) and modulator sections, respectively, is etched to access top side n-contacts. The

laser (and SOA) possesses a broad second mesa to enable lateral single mode operation apart

from mitigating nonradiative recombination paths and possible accelerated aging effects. The

EAM section features a narrow second mesa (structure below the ridge comprising the active

layer) to eliminate any parasitic capacitance due to finite lateral conductivity.

After depositing the n-type contact pads, the n++−doped region is etched underneath the

EAM feedlines to mitigate pad capacitance and thus improving the high-speed performance.

The entire structure is passivated and planarized by benzocyclobutene (BCB). In addition,

the BCB polymer reduces the capacitance of the EAM and serves as a platform for forming

the p-contacts. The final front-side process forms the p-type contact pads and the opening

of the BCB above the n-type contact pads. After wafer thinning and cleaving, the laser and

modulator facets are high and anti-reflection coated, respectively. (For EML-SOAs, the SOA

facet is anti-reflection coated).

Finally, the devices are mounted p-side up on copper (Cu) heat sinks for further investiga-

tions. Typical lengths of laser, modulator and SOA sections are 380µm, 120µm and 500µm,

respectively.

Fig. 2.4 shows a schematic view of the device after complete fabrication. The laser and am-

plifier (optional) sections feature contacts for continuous wave operation, i.e., direct current

(DC) contacts. The EAM features an optimized traveling wave electrode (TWE). Electri-

cal signal injected at the input port of the traveling wave electrode travels along the ridge

10 Chapter 2. Device Principle

Lasercurrent

Electricalsignal-out

Electricalisolations

BCB

Electricalsignal-in

Amplifiercurrent

p-contact

n-InP

p-InP

MQWactive layer

Semi-insulatingsubstrate

n-contact

Third mesa

Second mesa

(First mesa)Ridge

Fig. 2.4: Schematic illustration of a fabricated device consisting of laser, modulator and amplifier(optional) sections.

and modulates the optical wave that is guided below the ridge. The electrical wave exiting

the TWE is terminated with a matched resistor to suppress electrical reflections. As noted

earlier, the multiple quantum well (MQW) active layer (indicated by the two dark lines in

Fig. 2.4) is identical in all the sections of the device.

Chapter 3

Theory

This chapter discusses some of the important theoretical aspects that are exploited for inte-

grated EML structures. The most important property of the device, the electroabsorption

effect is briefly presented for bulk materials and quantum wells. General theory of optical

gain in quantum well structures is briefly presented. Commonly known rate equations are

also given for completeness.

After providing an overview of the above mentioned material properties, device oriented

properties are introduced. Waveguiding in the integrated device is briefly discussed. Sub-

sequently, the basic theory of coupled mode equations and its application to DFB lasers is

presented. Important expressions used for interpreting measurement results encountered in

this work are described using qualitative illustrations.

Frequency chirping properties of the device are discussed in a somewhat detailed fashion

emphasizing the main objective of this work. The relationship between absorption changes

and refractive index changes of the material is highlighted using the Kramers-Kronig rela-

tions. The separation of the DFB wavelength from the photoluminescence (PL) maximum

- the wavelength detuning - emerges as one of the important critical parameters in device

design. This is illustrated using a simple calculation. Besides insertion loss and extinction,

the resulting frequency chirp is shown to be strongly wavelength dependent.

Finally, from a system point of view, dispersion of optical fibers and important noise mech-

anisms in optical detection are presented.

3.1 Field induced absorption

Electroabsorption is the change in absorption coefficient of a material under the influence of

an external electric field. This effect is exploited for the fabrication of modulators.

11

12 Chapter 3. Theory

Franz-Keldysh effect:

The simplest form of electroabsorption is observed in bulk semiconductors whereby an exter-

nal electric field results in absorption of photons for energies lower than the bandgap energy

at equilibrium. This effect is known as the Franz-Keldysh effect. The Franz-Keldysh effect

is often exploited for modulators designed for operating over a wide wavelength range of

interest, typically 40–50 nm [20].

__

Conductionband

Valenceband

Ener

gy

Space

EgE -g

dT

whwh

whwh

__

E

Fig. 3.1: Schematic illustration of the Franz-Keldysh effect observed in bulk semiconductors.Absorption occurs for photons of energy lower than the bandgap energy of the semiconductorunder the influence of an external electric field.

Fig. 3.1 shows the schematic band diagram under the influence of a reverse bias. In the

absence of a photon, the valence band electron has to tunnel through a triangular barrier

of height Eg and thickness dT, given by dT = Eg/q|~E|. With the assistance of an absorbed

photon of energy ~ω, the tunneling barrier thickness is reduced to dT = (Eg − ~ω)/q|~E|,and the valence electron can easily tunnel to the conduction band. The net result is that a

photon of energy ~ω < Eg is absorbed. Hence, this effect also came to be known as photon

assisted tunneling. Put in other words, absorption of photons lower than the bandgap energy

can be controlled by an external electric field.

Quantum confined Stark effect:

Electroabsorption in quantum wells is much more pronounced due to the confinement of elec-

tron and hole wavefunctions within the wells. The electron ground state Ee1 and heavy hole

3.1. Field induced absorption 13

(HH) ground state Ehh1 in a quantum well are schematically shown in Fig. 3.2. With the ap-

plication of an electric field perpendicular to the plane of the quantum wells, the electron and

hole wavefunctions are displaced in such a way that the energy difference E21 ≡ Eg+Ee1−Ehh1

becomes smaller. This effect is termed as the quantum confined Stark effect (QCSE) [3]. The

QCSE effect manifests itself as a shift of the absorption edge toward longer wavelengths in

the EAM absorption spectra.

Eg

Ee1

Ehh1

Ec

Ev

Electronwavefunction

= 0

Holewavefunction

E

E21

> 0E

Ec

Ev

E21

Fig. 3.2: Schematic illustration of the energy bands in the absence of an electric field (left) andthe effect of an electric field |~E| perpendicular to the plane of the potential well (right). Tilting ofthe band edges results in a spatial overlap of the electron and hole wavefunctions in such a waythat the energy difference E21 becomes smaller.

A general expression for calculating material absorption α per unit length for a transition

from state E2 to E1 in quantum wells is given by [6]

α(E21) =q2

~

ǫ0cm20

(1

hν21

)

|MT(E21)|2 ρr(E21) (3.1)

where E21 is the energy difference (E2 − E1) between the transition states, q the electron

elementary charge, ~ the reduced Planck’s constant, ǫ0 the permittivity of free space, c the

velocity of light in free space and m0 the free electron mass. In Eq. (3.1) |MT (E21)|2 repre-

sents the transition matrix element and ρr (E21) the reduced density of states (DOS) for the

transition.

The transition matrix element |MT (E21)|2 in Eq. (3.1) takes the following two phenomena

into account [6]:


• polarization dependence of the strength of interaction of different states. e.g. For a

transverse electric (TE) wave (electric field parallel to quantum well plane), the strength

of interaction between the conduction band and heavy hole valence band states is 1/2,

whereas for a transverse magnetic (TM) wave (magnetic field parallel to quantum well

plane) it is zero. The magnitude of interaction for different states can be found, for

instance, in Refs. [6, 35].

• conservation of momentum, restricting the type of states which can interact. Popularly

called as the k-selection rule, it dictates that only transitions with identical k-vectors

can form a transform pair, thereby defining the allowed and forbidden transitions1.

For quantum well structures, the reduced density of states ρr (E21) is expressed as [6]

ρr(E21) =m∗

r

π~2dQW

(3.2)

where m∗

r is the reduced effective mass and dQW the thickness of the quantum well.

3.2 Optical gain

Material gain can be defined as the rate of growth of photon density per unit length of light

propagation along some direction in the medium. Gain at a given photon energy hν is ob-

tained by multiplying the absorption coefficient (at that particular photon energy) with the

Fermi factor (f2 − f1). The quantities f2 and f1 represent the Fermi occupation probabilities

of the electron and heavy hole ground states, respectively. They are related to the conduction

band and valence band quasi-Fermi levels EFc and EFv, respectively as [6]

f1 =1

exp [(E1 − EFv)/kBT ] + 1(3.3)

f2 =1

exp [(E2 − EFc)/kBT ] + 1(3.4)

where kB is the Boltzmann constant and T is the temperature in Kelvin.

Under strong pumping conditions, (f2−f1) becomes positive and one speaks from population

inversion for the transition energy E21. This pertains to the condition that the separation of

the quasi-Fermi levels ∆EF is such that [6]

EFc − EFv ≡ ∆EF > E21 (3.5)

1Neglecting valence band mixing effects which enable forbidden transitions at larger k-vectors away fromthe Γ-point [27].

3.3. Optical waveguiding 15

This implies that an incoming photon of energy hν corresponding to the transition energy

E21 will be amplified due to the stimulated emission process. Thus, using the expression for

α in Eq. (3.1), the net optical gain available per unit length is obtained by multiplying the

material absorption with the Fermi factor, (f2 − f1) as [6]

g(E21) = α(E21)·(f2 − f1) (3.6)

where the Fermi factor depends on the injection level. Taking the energy uncertainty of

the electron states into account, one can expect that the gain contribution at a particular

photon energy is contributed by all the transition pairs clustered within the energy uncer-

tainty width. Thus the total gain is obtained by summing the contributions of all subband

transitions. This broadening is described by the lineshape function L (hν) describing the

probable energy distribution of each transition pair. The complete gain spectrum is then ob-

tained by integrating g(E21) over all transition energies weighted by the appropriate lineshape

function [6].

g(hν) =

∫

g(E21) .L (hν − E21) dE21 (3.7)

Usually, the lineshape function is approximated by a Lorentzian function.

3.3 Optical waveguiding

The interaction of an optical wave with a given medium is exploited in active semiconduc-

tor devices for practical applications such as light generation or modulation. The medium

can be an amplifying one with a feedback mechanism (laser), a bias dependent absorbing

waveguide (EAM) or simply provide amplification (SOA). In all these cases, the individual

device sections, besides other functionalities, have to guide the optical wave counteracting

diffraction effects. A simple picture of waveguiding in one-dimension (1D) consists of a core

of refractive index (n′

core) surrounded by a cladding layer (n′

clad) on the top and a substrate

at the bottom (n′

sub) as schematically shown in Fig. 3.3.

Core

Cladding

SubstrateI

II

III

n clad

n core

n sub

x

z

y

Fig. 3.3: Schematic of a three-layer slab waveguide. Real part of the refractive indices are assumedto be uniform along the y-axis and the propagation direction z-axis.

The refractive indices of the core, cladding and substrate layers are such that

n′

core > n′

sub ≥ n′

clad (3.8)


The refractive indices of the cladding and substrate, in general, can be different. An optical

wave launched into the core of the waveguide will be guided if the propagation constant β of

the mode satisfies the following condition [36]

k0n′

sub < β < k0n′

core (3.9)

where k0 ≡ 2π/λ is the free space propagation constant. For the condition of guided modes,

the values of the allowed β (different propagation modes) are discrete. These allowed solu-

tions are called the eigenvalues and the corresponding modes are called the eigenmodes. The

number of confined modes depends on the core thickness, the frequency and the refractive

indices of the individual layers.

For the general case of a waveguide, the real part of the refractive index profile can vary

both transversally and laterally; i.e., the refractive index profile is expressed as n′(x, y). The

eigenmodes are obtained by solving the following wave equation [36]:

∇2TE(x, y) +

[n′2(x, y)k2

0 − β2]E(x, y) = 0 (3.10)

where E(x, y) represents the field distribution and ∇2T ≡ ∂2/∂x2 + ∂2/∂y2 is the transverse

Laplacian operator in Cartesian coordinates. The solutions to the wave equation are ob-

tained by looking for oscillatory solutions in the core and decaying solutions in the cladding

and substrate regions which simultaneously satisfy the boundary conditions at the interfaces.

The transversal confinement in the integrated device (see Fig. 2.4) is accomplished by the

high index separate confinement heterostructures surrounded by low index cladding layers.

x

z

y

I

II

III

n core

n sub

In clad Guided mode

Fig. 3.4: Schematic of a ridge waveguide structure providing optical confinement in the lateraly-direction.

The lateral confinement of the optical mode is achieved by etching a ridge waveguide structure

as schematically shown in Fig. 3.4.

Confinement factor

The confinement factor Γ represents the fraction of the optical energy that overlaps with the

active region. It is a convenient measure of expressing the modal properties of the guided

wave. It is given by the following relation [3]:

3.4. Material system 17

Γ =

∫ ∫

active|Ey(x, y)|2 dx dy

∞∫

−∞

∞∫

−∞

|Ey(x, y)|2 dx dy

(3.11)

For instance, the net gain available for an optical mode is the fraction of the mode which

interacts with the carriers in the active region and thereby contributing to the stimulated

emission process. Thus, the modal gain 〈g〉 is obtained by simply weighting the material gain

g with the confinement factor Γ as 〈g〉 = Γ·g. Similar definitions apply to modal absorption,

modal refractive index values or changes in these quantities.

〈α〉 = Γ·α〈∆α〉 = Γ·∆α

〈n′

eff〉 = Γ·n′

eff (3.12)

Typical values of Γ realized for the fabricated devices lie between 10 − 13%.

3.4 Material system

The integrated device structures investigated in this work are based on the InGaAlAs/InP

material system. The InGaAlAs/InP material system features a large conduction band offset

∆Ec and a small valence band offset ∆Ev compared to the traditional InGaAsP/InP material

system [37]. The band offsets of both the material systems have been qualitatively sketched

in Fig. 3.5.

+

__

InGaAlAs

Ec

Ev

EbarEg

_Electron

+ Hole

Ec

Ev

InGaAsP

Ec

Ev

InGaAsP

_

+

Fig. 3.5: Schematic comparison of conduction and valence band offsets between InGaAsP andInGaAlAs material systems. The InGaAlAs material system offers superior performance in thelaser and EAM sections due to larger conduction band offset and smaller valence band offset.

The ratio of the conduction band offset ∆Ec to the total band offset, i.e., ∆Ec + ∆Ev

gives a measure of the electron and hole confinement in the conduction and valence bands,


respectively. It is written as

Ec,offset =∆Ec

∆Ec + ∆Ev

(3.13)

In the case of InGaAlAs material system, ∆Ec and ∆Ev correspond to 182 meV (≈ 252 nm at

1310 nm) and 119 meV (≈ 165 nm at 1310 nm), respectively [38]. Substituting the values in

Eq. (3.13) yields a value of 0.65 for Ec,offset. This can be contrasted with the value obtained

for the InGaAsP material system which is close to 0.4 [39].

The incorporation of the aluminum (Al) containing material system for device fabrication

offers the following advantages. In the laser section, the large conduction band offset of-

fers superior electron confinement [27, 40]. Hence, in general, temperature stability and low

threshold currents can be achieved. In the modulator section, a large conduction band dis-

continuity leads to stable excitons, i.e., excitons with smaller linewidths at room temperature

and thus giving rise to steep absorption slopes. In addition, a smaller valence band disconti-

nuity in the EAM section enhances fast removal of holes [41, 42] from the valence band and

thereby increasing the modulation bandwidth.

3.5 Distributed feedback lasers

A diode laser incorporates an optical gain medium, pumped by electrical energy, in a resonant

optical cavity. In a Fabry-Perot laser, a simple form of optical feedback can be realized by

cleaving the facets to form an optical resonator. The mirror loss (correspondingly the mirror

reflectivity) of the resonant modes stays nearly constant over the available gain spectrum

and the laser oscillates in several longitudinal modes. As a result, the threshold gain of the

various modes is predominantly determined by the modal gain alone.

For high-speed optical communications, it is highly desirable that the laser oscillates in a

single longitudinal mode to overcome modal noise and modal dispersion effects. Such a

frequency selectivity can be achieved by varying the mirror loss of the possible modes. A

distributed feedback laser operates on this principle. Frequency selectivity is achieved by

introducing a periodic perturbation of the refractive index, which in general can be complex.

As the name reveals, the feedback mechanism is distributed over the active region. The

principle of operation of a DFB laser is discussed in the following.

Consider a waveguide structure incorporating a modal gain 〈g〉 and having an index pertur-

bation with a period Λ placed above the active region as shown in Fig. 3.6. Let n′eff and n′

grat

be the effective refractive indices of the waveguide and the grating material, respectively. Let

Γ and Γgrat denote the overlap of the mode with the active layer and the grating respectively.

The fundamental TE mode traveling in the z-direction can be expressed by the scalar wave

equation as [6]

3.5. Distributed feedback lasers 19

∇2TE(x, y) +

[n′2(x, y, z)k2

0 − β2]E(x, y) = 0 (3.14)

where E(x, y) represents the field distribution, ∇2T ≡ ∂2/∂x2+∂2/∂y2 is the transverse Lapla-

cian operator in Cartesian coordinates, n′(x, y, z) the real part of the refractive index profile,

k0 ≡ 2π/λ the free space propagation constant and β the mode propagation constant. The

z-dependence of the real refractive index allows for any perturbation along the propagation

direction.

The period of the grating Λ along with the effective index determines the Bragg wavelength

λb = λ/n′

eff = 2Λ/p, where p is an integer indicating the order of the grating. In this work,

only real index gratings of first order (p = 1) are dealt with. Maximum reflectivity occurs

for the Bragg wavelength which is termed as the Bragg condition. The threshold gain of

the various modes is now a strong function of the relative difference between the Bragg

wavelength characterized by the Bragg detuning parameter δb = β − βb, where βb ≡ pπ/Λ

is the Bragg propagation constant.

+grating

active layer

z0 L

Fig. 3.6: Schematic of a distributed feedback laser showing the periodic index grating positionedabove the active layer. The overlap of the fundamental mode with the active region and the gratingis also shown schematically.

An expression for the coupling strength κ, which describes the field reflectivity obtained per

unit length, for a small cosinusoidal index perturbation n′ = ∆n′grat cos (2πn′

effz/Λ) is given

by [6]

κ =

(n′

grat

n′eff

)(π

λ

)

Γgrat∆n′grat (3.15)

where ∆n′grat is the half peak to peak real refractive index variation defining the grating.

The net field in the waveguide structure, for z ≤ L, can be expressed as a sum of two

counterpropagating modes as

E(z) = E+e−iβz + E−e+iβz (3.16)


where, E+ and E− are the forward and backward traveling waves, respectively. For clarity,

the transverse mode profile (x, y) of the fields in Eq. (3.16) has been suppressed. Restricting

close to the Bragg wavelength λb and assuming slowly varying envelope for the fields, one can

neglect their second derivatives. After substituting in the wave equation and comparing the

coefficients one obtains the following relationship for the counterpropagating modes as [43]

+dE+

dz=

(

〈g〉2

− iδb

)

E+ + iκE− (3.17)

−dE−

dz=

(

〈g〉2

− iδb

)

E− + iκE+ (3.18)

These are the coupled mode equations describing wave propagation in a medium having a

net gain and a periodic perturbation. The equations can be interpreted as follows: The rate

of change of the propagating modes with z is a sum of contributions of the modal gain 〈g〉,the detuning induced phase mismatch δb and the counterpropagating mode weighted by the

feedback factor κ. In the case of index gratings, the Bragg mode interferes destructively

for ideal anti-reflection coated facets. The two side modes positioned immediately close to

the Bragg wavelength are in resonance and experience identical threshold gain2 and oscillate

with equal amplitudes. In general, one could expect that the degeneracy is lifted when the

facets have different reflectivity values and/or the modes experience different gain values.

General rate equations

The operating characteristics of semiconductor lasers are described by a set of rate equations

that govern the interaction of photons and electrons inside the active region. The rate

equations provided in this section correspond to continuous wave operation of laser diodes.

The carrier density N in the active zone takes the form [6]

dN

dt=

ηiI

qVact

− N

τ− vggNp (3.19)

where ηi represents the internal quantum efficiency, the fraction of the terminal current con-

tributing to carriers in the active region, q the elementary charge and Vact the active volume.

N denotes the carrier density and τ the carrier life-time, which in general is a function of

carrier density N . vg is the group velocity of the optical mode, g the gain per unit length

and Np is the photon density.

The first term in Eq. (3.19) refers to the rate of generation of carriers in the active zone, the

second term refers to the rate of loss of carriers due to spontaneous bimolecular recombina-

tion coefficient (B) and nonradiative transitions comprising the defect (A) and Auger (C)

recombination coefficients. The carrier life-time is related to the carrier density through [6]

2Under identical gain values for the two degenerate modes.

3.6. Electroabsorption modulators 21

N

τ= BN2 + AN + CN3 (3.20)

The last term in Eq. (3.19) is the contribution of the carriers to the stimulated emission

process. The corresponding photon density in the active region can be written as [6]

dNp

dt= ΓvggNp + ΓβspRsp −

Np

τp

(3.21)

where Np is the photon density and Γ the confinement factor, the electron-photon overlap

factor. βsp represents the spontaneous emission factor, Rsp the spontaneous photon genera-

tion rate and τp the photon life-time in the cavity.

In Eq. (3.21) the first and second terms contribute to the photon generation rate through

stimulated and spontaneous emissions, respectively. The last term accounts for the rate of

loss of photons due to optical absorption or scattering and the useful portion of optical power

coupled out.

3.6 Electroabsorption modulators

Static intensity modulation performance

The static properties of an electroabsorption modulator are primarily characterized by the

residual absorption α0 and the absorption swing ∆α obtained for a given voltage change.

Both the quantities are specified at the operating wavelength λDFB usually at ambient tem-

perature conditions. The absorption quantities are weighted with the confinement factor to

obtain the respective modal properties. Fig. 3.7 shows schematic absorption spectra illus-

trating the above two quantities.

The optical output power levels in the ON and OFF states are given by

PON = ηcPin exp−〈α0〉LEAM (3.22)

POFF = ηcPin exp− [〈α0〉 + 〈∆α (V )〉] LEAM (3.23)

where Pin is the total power injected by the DFB laser diode into the EAM section, 〈α0〉 is

the modal residual absorption of the EAM section, 〈∆α(V )〉 is the bias dependent modal

absorption change. In Eqs. (3.22) and (3.23), LEAM refers to the length of the EAM section

and ηc is the coupling efficiency, for instance, in a single-mode fiber. Throughout this work,

unless otherwise specified, a single-mode lensed fiber with a coupling efficiency of ≈ 40 % was

used to collect the output power.


Abso

rpti

on 0V

-1V

Operatingwavelength

0

Wavelength

Fig. 3.7: Schematic absorption spectra of an electroabsorption modulator showing the residualabsorption α0 and an absorption swing ∆α, upon reverse biasing.

Static light extinction is given by the ratio of the power levels during the ON and OFF states

of the EAM. It is more common to report the values in the logarithmic scale as

Extinction ratio [dB] = 10 log

(PON

POFF

)

(3.24)

where PON and POFF represent the ON and OFF state power levels, respectively. The ab-

sorbed power in the EAM section is detected as a photocurrent according to

IEAM = ηabs Pin [1 − exp (−〈α〉LEAM)]( q

~ω

)

(3.25)

where ηabs is the fraction of power converted into electron-hole pairs and 〈α〉 is the sum of

the residual absorption and absorption change, i.e., 〈α〉 = 〈α0〉 + 〈∆α〉.

Dynamic intensity modulation performance

The dynamic intensity modulation response of an EAM is of prime concern in EML device

design. The frequency response of an EAM is primarily influenced by the following factors:

EAM capacitance: The total capacitance of the EAM decisively affects the modulation

bandwidth. The modulation bandwidth is limited by the resistance-capacitance (RC) time

constant of the EAM and thus inversely proportional to the capacitance. The capacitance

of the EAM can be estimated using the EAM dimensions and the intrinsic area thickness as

follows:

CEAM = ǫ0ǫrAEAM

dpin

(3.26)

where dpin is the intrinsic area thickness, AEAM is the EAM area contributing to capacitance

and ǫ0 and ǫr the permittivity of free space and relative permittivity, respectively. Since

3.6. Electroabsorption modulators 23

the modulation bandwidth of an EAM, among other factors, is inversely proportional to the

total capacitance (and hence AEAM), two EAM design modifications shall be considered in

the following to minimize AEAM:

(a) Etched-through EAM: Fig. 3.8 (a) shows a scanning electron microscope (SEM) image

of an EAM exploiting a conservative layout. The finite conductances indicated in the figure

arise from the p-doped layers above the grating layer positioned above the multiple quantum

well active layer.

finiteconductance

p-contact

ridge

junctioncapacitance

substratejunctioncapacitance

p-contact

ridge

substrate

(a) (b)

Fig. 3.8: Scanning electron microscope images of (a) a conservative EAM layout featuring finitelateral conductances above the multiple quantum well active layer (b) etched-through structureseliminating the lateral conductances.

In this work, etched-through structures possessing a narrow second mesa of width 2.2µm,

were employed in the EAM section. This eliminates the parasitic lateral conductance as

shown in Fig. 3.8 (b). However, for the etched-through geometries, the etching process has

to be carefully controlled in order to avoid surface roughness induced mode scattering losses.

Electricalsignal-out

BCB

Electricalsignal-in

p-contact

n-InP

p-InP

MQWactive layer

Semi-insulatingsubstrate

n-contactn-layer etchedbelow EAMfeed-lines

n-layer etchedbelow EAMfeed-lines

Fig. 3.9: Schematic illustration of a fabricated EML-SOA device featuring an etched-through EAMsection. The n-InP layer below the electrical feed-lines have been shown to be etched out, therebyminimizing the pad capacitance contribution.


(b) Semi-insulating substrate: A schematic view of a fabricated EML-SOA device featur-

ing an etched-through EAM section is shown in Fig. 3.9. The n-InP layer below the electrical

feed-lines have been etched out. This mitigates the feed-line (pad) capacitance [44, 45] and

thus leads to improved modulation bandwidths.

The above mentioned design modifications i.e., the etched-through EAM section and semi-

insulating (s.i.) substrate were adopted [34] to improve the modulation bandwidth of the

fabricated EML devices.

Impedance mismatch: Apart from the capacitance induced limitations of an EAM, the

bandwidth is also influenced by the total impedance Z of the device under operating condi-

tions. The use of semi-insulating substrates along with an optimized traveling wave (TW)

electrode configuration improves the impedance matching of the EAM in a 50 Ω environ-

ment [46].

3.7 Semiconductor optical amplifiers

A semiconductor optical amplifier (SOA) is essentially a laser diode (LD) with ideally no

feedback. SOAs are primarily characterized by the following parameters:

Gain bandwidth: The gain bandwidth ∆νg is defined as the full width at half maximum

(FWHM) of the gain spectrum. It is a measure of the range of frequencies (wavelengths)

that can be amplified with sufficient gain. The values of ∆νg for the SOAs studied in this

work lie in the range of 7 THz (≈ 55 nm at 1550 nm).

Gain coefficient: The frequency dependence of the gain coefficient values is characterized

by g(ω). The peak value of the gain coefficient is denoted by g0. The gain coefficient is ex-

pressed in inverse length units, more commonly in cm−1. It describes the rate of amplification

of the optical wave per unit length of propagation in the gain medium, i.e.,

dP

dz= Γ[g(ω) − αi]P = 〈g〉P (3.27)

where P is the optical power and αi the internal loss coefficient. The amplification factor

G(ω) is the ratio between the output and input power levels. It is related to the gain

coefficient as G(ω) = exp [〈g〉LSOA].

Saturation output power: The power dependence of g(ω) is the origin of gain saturation

effects in a semiconductor optical amplifier. Gain saturation denotes the decrease of gain

when the power level becomes comparable to a certain power level, called the saturation

power Psat. For the case of optical frequency which experiences the peak gain g0, Eq. (3.27)

can be written as

3.8. Frequency chirp 25

dP

dz=

〈g0〉P1 + P/Psat

(3.28)

The denominator in Eq. (3.28) decreases the available again when the power levels become

comparable to the saturation power.

Noise figure: The degradation of signal to noise ratio during signal amplification is at-

tributed to the amplified spontaneous emission (ASE) noise. ASE is characterized by am-

plifier noise figure Fn. The theoretical limit of Fn is ≈ 3 dB. Typical values of Fn for SOAs

can be as large as 6–10 dB. The noise figure, in general, is dependent on the amplifier pump

current and the operating wavelength.

When the reflectivity of the facets is < 0.1 %, the optical wave predominantly advances in the

forward direction with simultaneous amplification. Such SOAs are also popularly referred

to as traveling-wave amplifiers (TWAs) [28]. A superior anti-reflection (AR) coating also

suppresses the amplitude of gain ripples that might otherwise be encountered. EMLs inte-

grated with semiconductor optical amplifiers, emitting in the 1550 nm wavelength window,

are studied in this work.

3.8 Frequency chirp

Frequency chirp refers to the instantaneous variation of the optical carrier frequency upon

intensity modulation. In optical communication systems, this might seriously limit the trans-

mission performance due to the accompanied dynamic spectral broadening. Hence a detailed

analysis and a comprehensive understanding of the device chirping behavior becomes essen-

tial to estimate the maximum distance-bandwidth product.

The sign and magnitude of the refractive index change (electrorefraction) encountered at the

wavelength of operation determines the final chirping behavior. The electrorefraction spectra

are inherently related to the electroabsorption spectra of the EAM through the Kramers-

Kronig relations. In the following, the Kramers-Kronig relations are presented for a medium

that can be characterized by a complex susceptibility. A derivation of the Kramers-Kronig

relations can be found in Appendix B.

Kramers-Kronig relations

The Kramers-Kronig relations relate the real and imaginary parts of the complex suscepti-

bility of a medium. The complex susceptibility χ is, in general, a function of the frequency

ν expressed as χ(ν) = χ′(ν) + iχ′′(ν). The real and imaginary parts χ′(ν) and χ′′(ν) are

related as [2]


χ′(ν) =2

πP

∞∫

0

ν ′χ′′(ν ′)

ν ′2 − ν2dν ′ (3.29)

χ′′(ν) =2

πP

∞∫

0

νχ′(ν ′)

ν2 − ν ′2dν ′ (3.30)

Eqs. (3.29) and (3.30) form the Kramers-Kronig relations with P being the Cauchy princi-

pal value of the integral. The relations show that a knowledge of the behavior of one of the

quantities over the complete spectrum enables the determination of the other.

The real and imaginary parts of the complex refractive index is a function of the real and

imaginary parts of the complex susceptibility. This is also applicable for changes in the

above quantities. The absorption change ∆α of the EAM is usually extracted from pho-

tocurrent absorption measurements of as-grown MQW structures. Thus, with the use of the

Kramers-Kronig relations (cf. Appendix B), the refractive index change ∆n′ as a function of

wavelength and voltage is calculated using [3, 47]:

∆n′(λ, V ) =λ2

2π2P

∞∫

0

∆α(λ′, V )

λ2 − λ′2dλ′ (3.31)

assuming fairly constant carrier density and temperature in the EAM section. In Eq. (3.31)

λ is the wavelength of interest and λ′ is a variable.

The specific profile of the electroabsorption spectrum at various bias voltages in conjunction

with the operating wavelength governs the sign and magnitude of the refractive index change

∆n′. This is illustrated in Fig. 3.10. Regions marked as ‘A’ and ‘C’ in Fig. 3.10 (a) contribute

negative values to the integrand in Eq. (3.31) whereas region ‘B’ contributes positive values.

The refractive index change at the operating wavelength λDFB is proportional to the sum

of contributions from all the three regions A, B and C. As can be seen in Fig. 3.10 (b), the

contribution of the absorption changes (at λDFB) which occur far away from the band edge

becomes negligible. The predominant absorption contribution occurs close to the EAM band

edge.

Fig. 3.10 also illustrates the impact of the operating wavelength, i.e., the effect of wavelength

detuning (separation of the DFB wavelength from the photoluminescence maximum). For

instance, decreasing the effective detuning, decreases the positive contribution of region ‘B’

while simultaneously increasing the negative contribution from ‘C’.

3.8. Frequency chirp 27

1200 1240 1280 1320 1360 14000

200

400

600

800

1000

Reverse biased

0V

C

B

A

DFB

Abso

rptio

n

[a

rb. u

nits

]

Wavelength [nm]

(a) Schematic absorption spectra

1200 1240 1280 1320 1360 1400-6

-4

-2

0

2

4

6

C

B

A

DFB

/(

2 DFB

-2 )

[arb

. uni

ts]

+ve contribution

-ve contribution

Kramers-Kronig integrand

Wavelength [nm]

(b) Kramers-Kronig integrand

Fig. 3.10: (a) Schematic EAM absorption spectra (b) corresponding contribution of absorptionchange to Kramers-Kronig integrand in Eq. (3.31). The refractive index change at the operatingwavelength λDFB is proportional to the sum of contributions of the different shaded areas. Forwavelengths far away from the absorption band edge of the modulator, the value of the integrandvanishes.

From the absorption change data, the change in the imaginary part of the refractive index

∆n′′ is calculated using the relation [3]

∆n′′ =λ

4π∆α (3.32)

Finally, the αH-parameter3, defined as the ratio of the change in real and imaginary parts of

the complex refractive index is given by [3]

αH =∆n′

∆n′′(3.33)

Typical absolute values of real and imaginary index changes encountered in multiple quantum

well active layers lie in the range of ≈ 2×10−2 for the range of wavelength detuning exploited

for the realization of devices and for voltage changes between 0 V and −2 V.

Relationship between intensity modulation & frequency modulation

In the previous subsection, the definition of chirp-parameter (αH) was introduced. The defin-

ition was completely based on the material properties, namely changes in complex refractive

index of the active layer.

3The chirp-parameter is only a ratio. Thus, a comparison of chirp-parameter values reported by differ-ent authors is justified only if the large-signal dynamic extinction ratio, which is proportional to ∆n′′ inEq. (3.33), is explicitly specified at the operating wavelength apart from using consistent expressions to avoidconfusion with regards to the sign of the chirp-parameter. One should also be aware that chirp-parametersmeasured using spontaneous emission spectra (e.g. exploiting resonance shift encountered in a Fabry-Perotlaser [48]) are not completely representative of the final chirping behavior.


However in a fabricated device, one observes the effect of these changes in terms of measurable

quantities. The real index change manifests itself as a phase change finally resulting in carrier

frequency deviations and the imaginary index change manifests itself as a finite extinction in

power. This section seeks to derive a relationship between the material properties and the

measurable quantities. To accomplish this task, an electroabsorption modulator is modeled

as an ideal intensity modulator cascaded in tandem with an ideal phase modulator (insertion

losses neglected) as illustrated in Fig. 3.11. Without loss of generality, we can assume that

the confinement factor equals 100%.

LEAM

idealintensity modulator

Input

LEAM

Output

EAM

LEAM

idealphase modulator

Fig. 3.11: Modeling an electroabsorption modulator as a combination of intensity modulator andphase modulator cascaded in tandem.

Let a CW source provide input to the EAM and let an arbitrary voltage waveform V (t)

modulate the EAM. The time dependent voltage modulates the complex refractive index

n = n′ + in′′. The instantaneous optical field Eopt(t) at the output of the EAM can be

expressed as

Eopt(t) = Eopt expik0n(t)LEAM (3.34)

= Eopt exp−k0n′′(t)LEAM

︸︷︷︸

amplitude modulation

· expik0n′(t)LEAM

︸︷︷︸

phase modulation

(3.35)

with Eopt as the complex amplitude taking initial phase of the carrier frequency into account

and k0 = 2π/λDFB the propagation constant of the operation wavelength. The first term in

Eq. (3.35) denotes amplitude modulation due to imaginary index variations and the second

term phase modulation due to real index variations. The time dependent intensity Iopt(t)

and phase4 φ(t) are given by

4For simplicity, the additional phase term due to the carrier frequency (ωct) has been suppressed, sinceit does not affect the frequency changes. Hence, by the term ‘phase’ we mean only the phase deviations thatcontribute to the chirping behavior.

3.9. Dynamic frequency modulation performance 29

Iopt(t) =∣∣∣Eopt

∣∣∣

2

exp−2k0n′′(t)LEAM (3.36)

φ(t) = k0n′(t)LEAM (3.37)

The derivative of the intensity and phase terms is then expressed as

dIopt(t)

dt= Iopt(t) (−2k0LEAM)

[dn′′(t)

dt

]

(3.38)

dφ(t)

dt= k0LEAM

[dn′(t)

dt

]

(3.39)

Using the definition of chirp-parameter from Eq. (3.33), the time dependent chirp-parameter

can be written using the index variations as follows:

αH(t) =

[dn′(t)

dt

]/[dn′′(t)

dt

]

(3.40)

Using Eqs. (3.38) and (3.39) in conjunction with the time dependent chirp-parameter in

Eq. (3.40), one can immediately find a relationship between the time dependent phase of the

output field and the intensity variation as

−dφ(t)

dt= ∆ω(t) =

αH(t)

2Iopt(t)

[dIopt(t)

dt

]

(3.41)

In practical experiments, one usually measures power changes P (t) rather than intensity

changes. Rewriting Eq. (3.41) in terms of power and using ω = 2πν we obtain,

∆ν(t) =αH(t)

4π

[1

P (t)

(dP (t)

dt

)]

(3.42)

=αH(t)

4π

[d ln P (t)

dt

]

(3.43)

Eq. (3.43) is an important relationship relating the carrier frequency deviations with the

power variations through the time dependent chirp-parameter αH(t).

3.9 Dynamic frequency modulation performance

Frequency chirp, as mentioned earlier, refers to the instantaneous variation of the optical

carrier frequency upon intensity modulation. In general, it consists of adiabatic and tran-

sient components. A schematic illustration of adiabatic and transient chirp components

accompanying intensity modulation is shown in Fig. 3.12.


Time

Transient chirp

Adiabaticchirp

Inte

nsi

tyC

arri

er f

requen

cy

ON

OFF OFF

Fig. 3.12: Schematic illustration of adia-batic and transient chirp components accom-panying intensity modulation of light in anEAM. Adiabatic chirp refers to carrier fre-quency difference between the ON and OFFstates whereas transient chirp refers to fre-quency changes encountered during rise andfall times of the pulse.

Adiabatic chirp:

Adiabatic chirp refers to the frequency difference between the ON and OFF states. Con-

tribution to adiabatic chirp can be due to one or more of the following as illustrated in

Fig. 3.13.

active layer

DFB Laser EAM

Forward bias Reverse bias

Thermal crosstalk

Optical feedback

Electrical crosstalk

Light output

AR

coat

ed

HR

coat

ed

Fig. 3.13: Schematic illustration of adiabatic chirp that might occur due to optical feedback,electrical crosstalk and thermal crosstalk in integrated laser-modulator structures. The rear side ishigh-reflection (HR) coated and the front side is anti-reflection (AR) coated.

(a) Optical feedback: Due to residual reflection on the AR coated facet (Fig. 3.13), some

light might be unintentionally reflected back into the laser cavity which is termed as optical

feedback. Even small amounts of optical feedback can influence the photon density within the

laser cavity and thereby influence the carrier density as governed by the laser rate equations.

Such changes in carrier density inevitably result in refractive index changes thereby leading

to emission frequency changes or adiabatic chirp.


(b) Electrical crosstalk: Insufficient electrical isolation between the laser and modulator

sections can lead to additional frequency chirping. This occurs because, voltage signal applied

to the electroabsorption modulator influences the laser current through finite conductance

(imperfect isolation) which has the effect of direct laser modulation.

(c) Thermal crosstalk: Thermal crosstalk is the phenomenon by which heat generated in

one of the sections of an integrated device influences the adjacent section [49] resulting in a

refractive index change. The effect generally manifests only at low data rates (≈Mbps) due

to the large thermal time constants in comparison to the bit rates of interest investigated here.

Transient chirp:

Transient chirp is caused by the parasitic refractive index modulation accompanying the bias

induced absorption change in the EAM. A schematic of refractive index modulation on an

incoming optical carrier wave is shown in Fig. 3.14. Physically, the optical length of the

EAM section is modulated by ∆n′ ×L which can be thought of as varying the length of the

EAM section keeping the refractive index of the waveguide constant (Fig. 3.14). As a result,

the output wave advances rapidly or slowly for a defined period of time as dictated by the

voltage signal profile. This phase modulation results in transient frequency chirp.

Slowoscillations

Rapidoscillations

Phase modulator

Time Time

Optical carrier Phase modulated wave

Lnx'

Fig. 3.14: Schematic illustration of phase modulation imposed on a carrier wave. Shown are therapid and slow oscillations of the carrier wave due to refractive index modulation.

The transient chirp can be quantitatively described as follows. The phase change encoun-

tered, ∆φ(t), is proportional to the length of the EAM section LEAM (which accounts for the

phase modulation), the confinement factor Γ and ∆n′. Mathematically, it can be expressed

by the relation


∆φ(t)∣∣∣0:−V

=

(2π

λDFB

)

LEAM Γ∆n′(t)∣∣∣0:−V

; V > 0 (3.44)

=

(2π

λDFB

)

LEAM〈∆n′(t)〉∣∣∣0:−V

(3.45)

with the temperature being constant. Since the derivative of the transient phase manifests

itself as frequency changes one can conclude that the transient chirp depends on

• active material properties (voltage dependency)

• device design parameters (wavelength detuning, EAM length, confinement factor5)

• magnitude of voltage swing

• modulating signal waveform (equivalently waveform steepness)

The steeper the drive signal, the larger is the phase change in a given interval of time and

hence maximum is the frequency deviation.

The magnitude and sign of the transient chirp predominantly govern the propagation of

modulated signals along a link. The relationship between the sign of the chirp-parameter

and the frequency changes encountered within a pulse is schematically illustrated in Fig. 3.15.

For the case of QCSE effect with uncoupled QWs (negligible interaction between the wave-

functions of adjacent wells) and the range of detuning exploited for the realization of the

devices, the change in imaginary index is always positive. This condition is also fulfilled for

the range of bias voltage applied to the EAM. Thus the sign of the chirp-parameter for prac-

tical measurements, is solely determined by the sign of real index changes. In the following

section, the effect of wavelength detuning on the frequency chirping behavior is discussed.

Effect of laser wavelength detuning

To reiterate, the separation of the DFB wavelength from the photoluminescence (PL) maxi-

mum is defined as wavelength detuning in this work. The operating wavelength of the DFB

laser has a profound impact on the chirping behavior, besides insertion loss and extinction. At

sufficiently large detuning values, the optical power increases; however, the operating wave-

length manifests positive chirp-parameters. Negative chirp-parameters are obtained only at

the expense of very high insertion losses.

For quantifying the above arguments, the different device properties of interest obtained

from an experimental absorption spectrum are presented in Fig. 3.16. For the illustration,

5The chirp-parameter itself is independent of the optical confinement factor Γ. But the total frequencychange is proportional to Γ through modal refractive index changes. The effect of confinement factor on thefrequency changes in Eq. (3.43) is implicitly included in the power variation term P (t).


Time

0V

-2V Voltage -2V

Intensity

Imaginaryindex change

Realindex change

Frequencychirp

HPositive behavior Negative H behavior

Fig. 3.15: Schematic illustration of positive and negative αH behavior upon intensity modulationof light. The sign of the chirp-parameter for the range of wavelength detuning exploited for devicerealization is solely determined by the sign of real index changes.

an EAM of length 130µm is assumed to be biased at −1 V and modulated with a peak to

peak voltage swing of Vpp = 2V. Let the optical power injected by the DFB laser into the

EAM section be 10 mW. One can observe that the absolute power coupled into the fiber

increases with increasing wavelength detuning due to the decaying residual absorption. The

corresponding insertion loss values can be read from the left-hand side axis of Fig. 3.16 (a).

At a wavelength detuning of 30 nm an ON state power of ≈ 0.8 mW and a static extinction

ratio of 17 dB is obtained, which can be regarded as an optimal wavelength detuning where

sufficient power and extinction are obtained simultaneously. The corresponding αH value is

positive and has a magnitude of ≈ 1.3.


-40 -20 0 20 40 60 80 1000

20

40

60

80

100

0

2

4

6

8

10LEAM = 130 µmPin = 10 mW

fiber = 40%

EAM

inse

rtion

loss

[dB]

Wavelength detuning [nm]

ON

sta

te p

ower

in fi

ber [

mW

]

(a) Insertion loss

-40 -20 0 20 40 60 80 1000

10

20

30

40

50

0

2

4

6

8

10LEAM = 130 µmPin = 10 mW

fiber = 40%

Stat

ic e

xtin

ctio

n ra

tio [d

B]


ON

sta

te p

ower

in fi

ber [

mW

]

(b) Static extinction

-40 -20 0 20 40 60 80 100-8-6-4-202468

-15

-10

-5

0

5

10

15

Vpp = 2VBias = -1V

H -

para

met

er


Pea

k ch

irp [G

Hz]

(c) αH−parameter

Fig. 3.16: (a) Experimental insertion loss (b) experimental static extinction (c) derived αH-parameter from photocurrent absorption measurements as a function of wavelength detuning. Theright-hand side axes of (a) and (b) show the expected optical power coupled into a single-modelensed fiber with a coupling efficiency of 40%, assuming an injected power of 10 mW by the DFBlaser. The expected peak frequency chirp is plotted in (c).

3.10. Phase modulation in semiconductor optical amplifiers 35

Assuming rise and fall times of ≈ 11 picoseconds (ps), which is a reasonable value for 40 Gbps

modulation and a modal refractive index change of 2.5 × 10−3 for 2Vpp (cf. Fig. 4.2 (c)), a

peak chirp of ≈ 7.5 GHz is to be expected by obtaining the time derivative of the phase in

Eq. (3.45). Increasing the reverse bias, say to −2 V, (i.e., modulation between −1 V and

−3 V) will decrease the magnitude of the chirp-parameter by half but the optical power de-

grades considerably. Similarly, at very low detuning values, say around 15 nm, zero or even

negative chirp-parameters are obtained at −1 V bias, but the insertion loss increases dra-

matically to about 35 dB. Thus, the very high insertion loss values at low detuning renders

this window unsuitable for practical device operation.

Further, we observe that the peak chirp remains practically constant assuming values of

≈ 7 GHz for wavelength detuning between 25–35 nm. The peak frequency chirp at 35 nm is

smaller in spite of the relatively larger chirp-parameter. This is simply a consequence of the

definition of the chirp-parameter which is proportional to the ratio of frequency excursion

to power extinction; i.e., the weak modulation at larger detuning apparently results in a

monotonic increase of the chirp-parameter.

Wavelength detuning 25 nm 30 nm 35 nm

EAM insertion loss (0 V) 12 dB 8 dB 5 dBON state power (0 V) 0.2 mW 0.8 mW 1.1 mWStatic extinction (0:−2 V) 29 dB 17 dB 10.6 dBChirp-parameter (0:−2 V) +0.9 +1.3 +1.5Peak chirp (0:−2 V) +6.5 GHz +7.5 GHz +6.2 GHz

Tab. 3.1: Select values of insertion loss, power, static extinction, chirp-parameter and peak chirpfrom Fig. 3.16.

Table 3.1 summarizes important device properties for three different detuning values read

from Fig. 3.16. One can notice that optimum output power and extinction are achieved

near a wavelength detuning of 30 nm. As a final remark, although negative chirp-parameters

reappear for wavelength detuning values larger than 50 nm (Fig. 3.16 (c)), there is hardly any

modulation of light as can be read from Fig. 3.16 (b). The fluctuations of absorption change

for detuning wavelengths above 60 nm cause fluctuations in the chirp-parameter data.

3.10 Phase modulation in semiconductor optical am-

plifiers

The self phase modulation (SPM) in a semiconductor optical amplifier [50] can be exploited

to compensate for a positively chirped signal from an electroabsorption modulator [51]. A

complete theoretical treatment of SPM in semiconductor optical amplifiers is beyond the


scope of this work. Thus, in this section, important expressions adopted from Refs. [50, 51]

are provided to estimate the additional chirp imposed by an SOA onto an incoming signal.

General expression for SOA chirp

The chirp-parameter αH,SOA of the active material exploited for gain in an SOA at the

operation wavelength, λDFB, can be written as [3, 6]

αH,SOA =

[〈dn′〉dN

]/[〈dn′′〉dN

]

(3.46)

where 〈dn′〉 and 〈dn′′〉 represent the modal change in real and imaginary parts of the complex

refractive index n = n′+ in′′. Let Pin be the optical power coupled into the SOA. The output

power Pout is then Pout = Pin exp 〈g〉LSOA, where 〈g〉 is the net modal gain and LSOA is the

length of the SOA section. Assuming a constant change in the carrier density N throughout

the length of the SOA, the chirp-parameter can be written in terms of the modal gain 〈g〉as [6, 7]

αH,SOA = − 4π

λDFB

[〈dn′〉dN

]/[〈dg〉dN

]

(3.47)

where the relation dn′′ = −(λ/4π)dg has been used at the wavelength of operation. With in-

creasing carrier density (i.e., increasing SOA pump current), the refractive index n′ decreases

while the gain g in Eq. (3.47) increases. Thus, the resulting chirp-parameter of the SOA is

positive which is purely a material property of a medium delivering gain. Since frequency

changes are directly related to the real index variations we rewrite Eq. (3.47) to obtain

〈dn′〉 = −λDFB

4παH, SOA〈dg〉 (3.48)

Multiplying and dividing the right-hand side of Eq. (3.48) by the change in carrier density

dN , and recognizing 〈dg〉/dN as the modal differential gain 〈a〉, the total phase change dφ

after propagation in an SOA of length LSOA can be written as

dφ = −αH, SOA

2〈a〉dNLSOA (3.49)

Using the relation between chirp-parameter αH, optical power P and phase φ

αH = −2P

(dφ

dt

)/(dP

dt

)

(3.50)

and Eq. (3.49) the additional chirp, αH, signal due to an SOA, onto an incoming signal can be

written as [51]

αH, signal = αH, SOA

[

dN

dP

]

P 〈a〉LSOA (3.51)

3.10. Phase modulation in semiconductor optical amplifiers 37

MQW active layer

DFB Laser EAM SOAp-doped

n-doped

Intensity

ILD VEAM ISOA

Real index changeencountered in anEAM imposing apositive chirp-parameter

Real index changeencountered in again saturated SOA

Time Time

light output

Fig. 3.17: Schematic illustration of chirp compensation of a gain saturated semiconductor opticalamplifier due to carrier density modulation. The signal leaving the modulator section is assumedto have a positive chirp.

Absence of gain saturation: In the absence of gain saturation, ideally there is no change

in the carrier density N , i.e., dN/dP in Eq. (3.51) is zero and the optical wave leaves the

SOA section after being amplified as noted earlier. In general, no gain saturation is observed

for very weak input signals and one speaks from small-signal gain delivered by an SOA.

Presence of gain saturation: At high optical power levels, typically above −5 dBm in

ridge waveguide structures, gain saturation occurs in an SOA. Under such saturation con-

ditions, carrier density modulation accompanies power changes. With increasing optical

power, the carrier density decreases and therefore the available gain g (gain saturation).

Thus, dN/dP in Eq. (3.51) becomes negative whereas the chirp-parameter of the SOA gain

medium αH, SOA remains positive, thereby resulting in a negative chirp-parameter.

The effect of gain saturation on the incoming signal is schematically illustrated in Fig. 3.17.

The signal leaving the modulator section is assumed to have a positive chirp. The real

refractive index changes dn′/dP in the SOA section is now positive (since dN/dP < 0) which

compensates for the real refractive index changes occurring in the EAM section. The net

effect is to reduce the positive chirping of the signal or even reverse the sign of the (effective)

chirp-parameter.


3.11 Optical fiber dispersion

When an electromagnetic wave interacts with the bound electrons of a dielectric, the medium

response, in general depends on the optical frequency ω. This property known as chromatic

dispersion, manifests through the frequency dependence of the refractive index n(ω). On a

fundamental level, the origin of chromatic dispersion is related to the frequency dependent

absorption characteristics of the optical fiber [28]. The resonance frequencies (in the absorp-

tion characteristics) correspond to enhanced absorption of electromagnetic radiation through

oscillations of bound electrons.

Fiber dispersion plays a critical role in propagation of short optical pulses because differ-

ent spectral components associated with the pulse travel with different group velocities.

Even when nonlinear effects are not important, dispersion-induced pulse broadening can be

detrimental and could severely restrict the performance of a telecommunication system [28].

Mathematically, the effects of fiber dispersion are accounted for by expanding the mode-

propagation constant β in a Taylor series about the carrier frequency ωc at which the pulse

spectrum is centered.

β(ω) = βc + β1(ω − ωc) +1

2!β2(ω − ωc)

2 + · · · (3.52)

where

βn =

(dnβ

dωn

)∣∣∣∣ω=ωc

with n = 0, 1, 2, . . . (3.53)

The parameters β1 and β2 are related to the refractive index n′ and its derivatives through

the relations [52]

β1 =1

vg

=n′

g

c=

1

c

(

n′ + ωdn′

dω

)

(3.54)

β2 =1

c

(

2dn′

dω+ ω

d2n′

dω2

)

(3.55)

where n′

g is the group index and vg is the group velocity. Physically, the envelope of an

optical pulse moves at the group velocity while the parameter β2 represents the dispersion of

the group velocity. This dispersion of the group velocity is responsible for pulse broadening

and hence β2 is referred as the group velocity dispersion (GVD) parameter.

The quantity dispersion coefficient Dλ (also called as dispersion parameter) usually expressed

in ps/(nm·km) is frequently used in the fiber-optics literature in place of β2. The dispersion

coefficient is a measure of the broadening of a pulse due to its finite spectral width over one

kilometer (km) of fiber propagation. The two quantities are related to each other as [2]

Dλ =dβ1

dλ= −2πc

λ2β2 ≈ −λ

c

d2n′

dλ2(3.56)

3.12. Noise in optical detection 39

1100 1200 1300 1400 1500 1600 1700-30

-20

-10

0

10

20

30

D < 0

2 > 0

D > 0

2 < 0

Normaldispersion

Anomalous dispersion

Dis

pers

ion

coef

ficie

nt

[ps/

(nm

.km

)]

Wavelength [nm]

Fig. 3.18: Dispersion coefficient as a function of wavelength for a standard single-mode fiber [53].

Standard single-mode fibers (SSMFs) show zero dispersion around 1300 nm wavelength and

≈+17 ps/(nm·km) around 1550 nm wavelength as shown in Fig. 3.18.

The influence of fiber dispersion on the pulse spectrum is given by the phase factor which

contributes to pulse distortion [54,55]:

Fiber phase factor = exp

(−iπλ2Dλp2f 2

mLfiber

c

)

(3.57)

with p being the order of the sideband and fm the modulation frequency. Dλ and Lfiber

represent the dispersion coefficient and the length of the fiber, respectively.

A negatively chirped pulse propagating in the 1550 nm wavelength window undergoes pulse

compression until it reaches its Fourier-transform limited pulse width. At this point, the

pulse spectrum is completely deprived of spectral chirp. Thereafter, fiber dispersion results

in pulse broadening.

3.12 Noise in optical detection

Noise can be defined as an energy distribution which adds to the target signal over the band-

width Bw of interest. In general, noise degrades or obscures the performance of a system.

Ideally a photodetector responds to a photon flux Φ (optical power P = hνΦ) by gener-

ating a proportional electric current Idet = ηqΦ = RP where R is the responsivity and η

the quantum efficiency. In reality, the device generates a random electric current I whose

value fluctuates above and below its average I ≡ Idet. These random fluctuations, as men-

tioned earlier, constitute noise. Noise is characterized by the variance of the photocurrent


σ2N,i = 〈(I(t) − I)2〉 where I(t) is the instantaneous photocurrent detected.

For signal detection (be it in a laboratory or after a finite transmission distance), an important

parameter used to characterize the performance of the whole system is the signal to noise

(SNR) ratio defined as [3]

SNR =signal power

noise power

=PS

PN

=I2RL

σ2N,iRL

=I2

σ2N,i

(3.58)

where PS and PN represent the power levels in the signal and noise, respectively and RL the

load resistance. Usually the SNR value is reported in the logarithmic scale. PN in Eq. (3.58)

constitutes the sum of contributions of different noise sources. Limiting ourselves to the

process of direct detection of signals (intensity modulated ON/OFF keying) employing p-i-n

photodiodes, and recognizing the fact that detection frequencies, as far as this work is con-

cerned lie in the range of few decades of GHz, shot noise and thermal noise are identified as

the two dominant noise sources6.

Shot noise:

The most fundamental source of noise is associated with the random arrivals of the photons

themselves. The photon noise of an ideal monochromatic laser beam is described by the

Poisson statistics [2]

p(n) =nn exp (−n)

n!, n = 0, 1, 2, . . . (3.59)

where p(n) is the probability of detecting n photons. Upon detection, every photoelectron-

hole pair generates a pulse of electric current of charge q and time duration τp in the external

circuit of the photodetector. A photon stream incident on a photodetector therefore results

in a stream of electrical pulses which add together to constitute an electric current. The

variance of shot noise current is given by [3]

σ2N, shot = (2qBw)I (3.60)

The shot noise current, apart from other parameters, depends on the charge of the carrier.

The noise current σ2N, shot would vanish if the elementary charge q tended to zero, for the

same assumed value of the average current I. Consequently, it is this quantized nature of

the charge and its transport which manifests itself as shot noise.

6Background noise (in the presence of extraneous sources), dark current noise (in the absence of extraneoussources), leakage current noise, 1/f noise dominating in the low frequency regime have been ignored.

3.12. Noise in optical detection 41

Thermal noise:

Yet additional noise introduced by the electronic circuitry associated with an optical receiver

results from the thermal motion of mobile carriers in resistive electrical elements at finite

temperatures. These motions give rise to a random electric current I(t) even in the absence

of an external electrical power source. The thermal current in a resistance RL is therefore a

random function I(t) whose mean value 〈I(t)〉 = 0. Thermal noise is also termed as Johnson

noise or Nyquist noise. It is worth noting that the average current in thermal noise is zero

whereas that of shot noise it is non-zero.

Using an argument based on statistical mechanics, it can be shown that a resistance RL at

a temperature T exhibits a random electric current I(t) characterized by a power spectral

density Si(f) as follows [28]:

Si(f) =4

RL

[hf

exp (hf/kBT ) − 1

]

(3.61)

where f is the frequency. In the frequency region f ≪ kBT/h, which is of principal interest

since kBT/h = 6.25 THz at room temperature, exp (hf/kBT ) ≈ 1 + hf/kBT so that

Si(f) ≈ 4kBT

RL

(3.62)

The thermal noise current variance σ2N, thermal is the integral of the power spectral density

over all frequencies within the bandwidth of the circuit Bw. For Bw ≪ kBT/h [28]

σ2N, thermal ≈

4kBTBw

RL

(3.63)

Thus, the total signal to noise ratio of an optical receiver is [28]

SNR =I

2

(4kBTBw

RL

)

+ (2qBw)I

(3.64)

where Eq. (3.64) constitutes shot noise and thermal noise contributions.

Chapter 4

Characterizing Frequency Modulation(FM) Properties

As introduced in the previous chapter, modulating the intensity of light in an electroabsorp-

tion modulator is accompanied by a parasitic refractive index modulation. The refractive

index modulation results in a phase modulation of light. Since the frequency of light is pro-

portional to the time derivative of its phase, phase modulation inevitably results in carrier

frequency excursions.

ReceiverTransmitter Link

IM

FM

Fiber transferfunction

IM = Intensity modulationFM = Frequency modulation

Inter symbolinterference

Link length

Dispersion coefficient

Bit rate

1 0 1

1 ? 1

Fig. 4.1: Schematic illustration of inter symbol interference (ISI) as a result of interaction betweentransmitter chirp and link dispersion.

A simple communication system consists of a transmitter, a link and a receiver. The to-

tal bandwidth of optical signals in such systems has to be kept to a minimum, in order to

42

43

minimize dispersion related pulse broadening effects. This is especially the case for trans-

mission in the 1550 nm wavelength window where the fiber dispersion is large, as noted

earlier. Frequency chirp and dispersion interact during propagation leading to time domain

pulse distortion which might result in inter symbol interference (ISI) as schematically illus-

trated in Fig. 4.1. Above a tolerable value of ISI, the individual bits cannot be detected

reliably thereby resulting in high bit error rate values. The transmission bandwidth in such

dispersion-limited systems can be significantly enhanced by way of

(a) tailoring the chirp properties of the transmitter such that the prechirped signal compen-

sates for the fiber dispersion up to a certain distance.

(b) dispersion management of the transmission link [28], i.e., deployment of dispersion com-

pensating fibers (DCF) along the link at specified intervals.

In order to gain insight into such frequency chirping properties, it becomes important to

study the chirping behavior which can also pave way for future optimizations. This chap-

ter focuses on three important methods invoked in this work to characterize the frequency

chirping properties of the EMLs. The first method starts with the photocurrent absorp-

tion measurements to extract the chirp-parameter. The other two techniques exploit the

frequency domain and time domain for chirp-parameter extraction. The chirp-parameter

values extracted in the latter two methods are performed after final fabrication of the device

and hence correspond to the chirping behavior at the wavelength of operation, i.e., at λDFB.

• The electrorefraction and the chirp-parameter behavior over the complete wavelength

spectrum can be calculated using the Kramers-Kronig relations introduced in Sect. 3.8.

The investigation is purely based on the static behavior of the device. In addition, the

measurement conditions pertain to negligible thermal effects. However, the method has

proved to be a good starting point in designing EML structures since it yields valuable

information regarding the chirping properties of the material.

• In frequency domain characterization schemes, the small-signal response after propaga-

tion through a dispersive link is used for chirp-parameter extraction [56]. The method

proves advantageous in estimating the chirp-parameter for specific bias voltages. It

also gives a simple estimate of the dispersion-limited link distance. Unlike methods

which exploit the relative sideband strength under large-signal modulation [57,58], the

small-signal method yields the sign of the chirp-parameter.

• The time domain method is dynamic in nature, in which the frequency chirp is evaluated

at every time point of the modulated optical wave. Most notably, the large-signal

frequency chirping is strongly dependent on the type of modulation signal used. For

instance, at high bit rates the modulating voltage waveform has steep edges (i.e., short

44 Chapter 4. Characterizing Frequency Modulation (FM) Properties

rise and fall times) which increase the magnitude of the frequency change. This can be

understood if one considers the fact that, the total refractive index change and hence the

associated phase change occurs in a very short interval of time which result in enhanced

chirping. Thus this method characterizes chirp under realistic modulation conditions.

Hence a significant part of this chapter is devoted to the design and description of

time-resolved chirp measurement method.

4.1 Chirp-parameter extraction from photocurrent ab-

sorption measurements

The photocurrent absorption measurements are used for the extraction of the static chirp-

parameter values. Using the change in absorption data in conjunction with Eq. (3.31), the

real index changes are calculated. Finally, the chirp-parameter values are calculated using the

Kramers-Kronig transformations given by Eq. (3.33) and plotted as a function of wavelength.

1310 nm Electroabsorption modulated lasers

Electroabsorption modulated lasers emitting in the 1310 nm wavelength window employed

in this work, feature a multiple quantum well active layer with 10 × 5 nm thick single type

QWs. The photoluminescence wavelength (λPL) at room temperature and under low excita-

tion conditions is 1285 nm. The thickness of the intrinsic area (total thickness contribution

from QWs, barriers and separate confinement heterostructures) is 300 nm. The operating

wavelength of the device is near 1310 nm.

Figs. 4.2 (a) and (b) show the experimental modal absorption spectra of a 1310 nm EML

and the corresponding absorption change, respectively, as a function of wavelength detuning

at room temperature. Figs. 4.2 (c) and (d) show the corresponding modal refractive index

variations and αH-parameter values calculated in accordance with Eq. (3.31) and Eq. (3.33),

respectively. The results are plotted as a function of wavelength detuning (separation of

the DFB wavelength from the photoluminescence maximum) for three different EAM bias

voltages −1 V, −2 V and −3 V.

Some interesting features can be inferred from the plot. Firstly, for wavelengths just above

the bandgap wavelength, αH assumes negative values where ∆n′ is negative and where the

residual absorption is also generally high. Such negative αH values, for instance whose

magnitudes are ≤ 1, are advantageous for links employing fibers having a positive dispersion.

Moving away from the band edge, αH crosses the zero line and increases gradually in the

positive direction. This is a direct consequence of the positive change of ∆n′ and decreasing

absorption swing at longer wavelengths. Secondly, close to the operating wavelength regime

of 1310 nm it assumes values around +1.0 and decreases for increasing reverse bias voltages.

4.1. Chirp-parameter extraction from photocurrent absorption measurements 45

Such a behavior predicts that under large-signal modulation conditions, one can expect an

effective positive αH for modulation voltages between 0 V and −2 V.

-80 -60 -40 -20 0 20 40 60 80 1000.0

0.5

1.0

1.5

2.0

2.5

3.01220 1250 1280 1310 1340 1370

PL = 1285nmdpin = 300nmT = 25°CMQW : 10x5nm

Mod

al a

bsor

ptio

n<

> [x

103 /c

m]


-2V-1V-3V0V

Wavelength [nm]

(a) Experimental absorption spectra [34]

-80 -60 -40 -20 0 20 40 60 80 100-1200

-800

-400

0

400

800

12001220 1250 1280 1310 1340 1370

Mod

al a

bsor

ptio

n ch

ange

<>

[1/c

m]


-3V-2V

-1V

PL = 1285nmdpin = 300nmT = 25°CMQW : 10x5nm

Wavelength [nm]

(b) Modal absorption change

-50 -40 -30 -20 -10 0 10 20 30 40 50 60-20

-15

-10

-5

0

5

101250 1270 1290 1310 1330

T = 25°C-3V-2V

-1V

Mod

al re

f. in

dex

chan

ge

<n'

> [x

10-3

]


Wavelength [nm]

(c) Modal refractive index change

-50 -40 -30 -20 -10 0 10 20 30 40 50 60-8

-6

-4

-2

0

2

4

6

81250 1270 1290 1310 1330

T = 25°C

H-p

aram

eter


-2V

-1V -3V

-3V

-2V

-1V

Wavelength [nm]

(d) αH−parameter

Fig. 4.2: (a) Experimental absorption spectra [34] (b) modal absorption change (deduced withrespect to absorption at 0 V) from photocurrent absorption measurements of a 1310 nm EML forthree different modulator bias voltages −1 V, −2 V and −3 V (c) Kramers-Kronig transformedmodal refractive index change and (d) deduced chirp-parameter.




in this work, feature a multiple quantum well active layer with dual quantum well type:

3×5 nm thick and 8×7.5 nm thick quantum wells.. The photoluminescence (PL) wavelengths

of 8 × 7.5 nm thick quantum wells and 3 × 5 nm thick quantum wells at room temperature

and under low excitation conditions are 1510 nm and 1540 nm, respectively. The wavelength

detuning, in this case, is defined from the shortest of the two PL wavelengths; i.e., from

1510 nm. The thickness of the intrinsic area (total thickness contribution from QWs, barri-

ers, spacers and separate confinement heterostructures) is 272 nm. The operating wavelength

of the device is near 1563 nm.

Figs. 4.3 (a) and (b) show the experimental modal absorption spectra of a 1550 nm EML

and the corresponding absorption change, respectively, as a function of wavelength detuning

at room temperature. Figs. 4.3 (c) and (d) show the corresponding modal refractive index

variations and αH-parameter values, respectively, calculated using the Kramers-Kronig trans-

formations. The results are plotted as a function of wavelength detuning for different EAM

bias voltages.

It is apparent from Fig. 4.3 (d) that a chirp-parameter value of +2.0 will be obtained if one

biases the EAM at −1 V (i.e., modulation between 0 V and −2 V for 2Vpp). This large pos-

itive value of the chirp-parameter is a direct consequence of the larger wavelength detuning

employed in comparison with the 1310 nm EML design. One can also observe that the magni-

tude of the chirp-parameter at the operating wavelength decreases gradually with increasing

reverse bias, for instance at −2 V bias (modulation between −1 V and −3 V for 2 Vpp) it as-

sumes about +1. With this information, it opens the possibility of increasing the reverse bias

to obtain reduced chirping if one could obtain sufficient extinction and average output power.

As a remark, in Sect. 3.8 the refractive index change at a given wavelength was introduced to

be calculated using change in absorption data from the entire spectrum. However in practice,

the absorption curves are obtained over a finite wavelength interval (ca. 200–250 nm) around

the wavelength of operation. The wavelength range chosen is sufficient for the calculation

of chirp-parameter values with good accuracy. For instance, extrapolating the ∆α curves

in Fig. 4.3 (b) results in zero absorption change only around 1170 nm. This additional area

(due to extrapolation) contributes to a modal refractive index change of −7.5 × 10−5 at the

DFB wavelength. This is two orders of magnitude less than the total modal refractive index

change. Put in other words, the extrapolated area contributes to a chirp-parameter change

of 8 × 10−3, which is negligibly small. The above argument was schematically illustrated

in Fig. 3.10 (b), where the negative contribution of area ‘A’ decreases rapidly as one moves

away from the absorption band edge of the electroabsorption modulator.

4.1. Chirp-parameter extraction from photocurrent absorption measurements 47

-80 -60 -40 -20 0 20 40 60 80 100 120 1400.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1460 1510 1560 1610

PL = 1510nm

dpin

= 272nmT = 25°CMQW: 3x5nm,8x7.5nm

-2V

-3V-1V

-4V0V

Mod

al a

bsor

ptio

n<

> [x

103 /c

m]


Wavelength [nm]

(a) Experimental absorption spectra [34]

-80 -60 -40 -20 0 20 40 60 80 100 120 140

-600

-400

-200

0

200

400

600

1460 1510 1560 1610

PL = 1510nm

dpin

= 272nmT = 25°CMQW: 3x5nm,8x7.5nm

-2V

-3V

-1V -4V

Mod

al a

bsor

ptio

n<

> [1/c

m]


Wavelength [nm]

(b) Modal absorption change

-50 -40 -30 -20 -10 0 10 20 30 40 50 60-15

-10

-5

0

5

101460 1480 1500 1520 1540 1560

T = 25°C

-2V-3V -4V

-1V

Mod

al re

f. in

dex

chan

ge<

n'>

[x 10-3

]


Wavelength [nm]

(c) Modal refractive index change

-50 -40 -30 -20 -10 0 10 20 30 40 50 60-8

-6

-4

-2

0

2

4

6

81460 1480 1500 1520 1540 1560

T = 25°C

-3V-2V

-4V-1V

-2V -3V

-4V-1V

H-p

aram

eter


Wavelength [nm]

(d) αH−parameter

Fig. 4.3: (a) Experimental absorption spectra [34] (b) modal absorption change (deduced withrespect to absorption at 0 V) from photocurrent absorption measurements of a 1550 nm EML fordifferent modulator bias voltages (c) Kramers-Kronig transformed modal refractive index changeand (d) deduced chirp-parameter.


4.2 Small-signal chirp

4.2.1 Principle of measurement

The small-signal chirp method, as the name implies, estimates the chirp-parameter of an

optical transmitter in conjunction with a dispersive link under small-signal modulation con-

ditions. The method is based on the fact that frequency chirp interacts with dispersion

thereby limiting the link distance, which appears as frequency dips during detection. The

principle of measuring small-signal chirp is described in the following.

Let us assume an EAM being modulated by a small electrical signal around some bias value

VEAM. The time dependent complex electric field Eopt(t) can be written as [20]

Eopt(t) =√

Iopt (t) expi[ωct + φ(t)] (4.1)

where Iopt (t) is the time varying intensity due to modulation around the bias point and ωc

the angular carrier frequency of light. An additional time dependent phase variation term

φ(t) has been introduced in Eq. (4.1). This time dependent phase term takes frequency chirp,

if any, into account which might accompany the intensity modulation.

Under the small-signal conditions assumed, the time varying intensity and phase terms in

Eq. (4.1) can be expanded as

Iopt(t) = Iopt [1 + m cos (2πfmt)] with m ≪ 1 (4.2)

φ(t) =αH

2ln Iopt(t) (4.3)

where m is the small-signal intensity modulation index which is assumed to be very low, Iopt

the average optical power and fm the modulation frequency of light. The time dependent

phase is coupled to intensity variations through the chirp-parameter introduced in Sect. 3.8,

Eq. (3.43).

Substituting the expressions for intensity and phase in Eq. (4.1) yields the desired electric

field as

Eopt(t) =√

Iopt [1 + m cos (2πfmt)] exp

i(

ωct +αH

2ln∣∣Iopt [1 + m cos (2πfmt)]

∣∣

)

(4.4)

Collecting like terms and rearranging one obtains

Eopt(t) =

Iopt [1 + m cos (2πfmt)](1+iαH)/2

exp(iωct) (4.5)

4.2. Small-signal chirp 49

which comprises a complex term modulating the carrier waveform. The complex envelope is

made of both intensity modulation (IM) and frequency modulation (FM) components. The

“1 + ” term in Eq. (4.5) contributes to the DC component in the Fourier space, representing

the average power. Multiplying the complex amplitude with the carrier frequency simply

shifts the DC component to the position of the carrier frequency.

The complex envelope function can be developed into a m power series1 to yield the Fourier

coefficients. Restricting to the first power of m, we obtain the complex amplitudes as

E−1 =√

Iopt m

(1 + iαH

4

)

Ec =√

Iopt

E+1 =√

Iopt m

(1 + iαH

4

)

(4.6)

where Ec represents the carrier frequency of light and E−1, E+1 represent the first lower

and the upper sidebands respectively. In Eq. (4.6) the real and imaginary parts of the field

amplitudes are a result of IM and FM respectively. The IM sidebands possess an even sym-

metry and the FM sidebands an odd symmetry with respect to the carrier frequency. Since

the intensity modulation index was assumed to be very small, the amplitudes in Eq. (4.6)

are identical [55]. For very high intensity modulation accompanied by frequency modulation,

the spectrum becomes increasingly asymmetric.

With the above formulation, one has complete information about the complex spectrum

exiting the EML. The influence of a transmission link on the input spectrum is obtained

by propagating all the frequencies along the fiber and finally detecting them. Since the

group index (n′

g) of a fiber is wavelength dependent (contributions of material dispersion and

waveguide dispersion), each of the frequency components in Eq. (4.6) travels with its own

propagation constant β along the fiber.

Letting the propagation constant of the carrier to be βc, the propagation constants of the first

upper and lower sidebands can be developed using Taylor series. Restricting the expansion

to the first three terms one can write

1Using the binomial expansion for complex powers [59]

(x + y)z

=∞∑

p=0

(z

p

)

xpyz−p with,

(z

p

)

=1

p!

p−1∏

r=0

(z − r) =z(z − 1)(z − 2) · · · (z − p + 1)

p!


β±1 = βc ±2πfm

vg

− πλ2Dλf2m

c(4.7)

where β+1 and β−1 are the propagation constants of the first upper and lower sidebands

respectively. The group velocity and dispersion coefficient of the mode are represented by

vg and Dλ, respectively. After propagating through the dispersive link, the first upper and

lower sidebands have acquired an additional phase proportional to β±1Lfiber. The electric

field spectra of the light wave after propagation through the fiber is then given by

Efiber = exp(iωct)

Ec exp[

i(−βcLfiber)]

+∑

p=−1,+1

Ep exp[

i(2πpfmt − βpLfiber)]

(4.8)

Eq. (4.8) is a compact expression which constitutes transmitter dependent chirp properties

and fiber specific dispersion properties. In addition, one can observe that the fiber length

Lfiber also influences the final phase of the electric field. At the receiver end, the magnitude of

optical field results in power variation for systems employing direct detection. The detected

photocurrent component Ifm,det at the modulation frequency is obtained by multiplying out

and collecting all the interference terms contributing to power at the modulation frequency

fm as

Ifm,det = Iopt m√

1 + αH2

∣∣∣∣cos

(πλ2DλLfiberf

2m

c+ arctan (αH)

)∣∣∣∣

(4.9)

The dispersion coefficient of the fiber Dλ in Eq. (4.9) is commonly expressed in units of

ps/(nm·km), its value depending on the wavelength of interest and the type of fiber used.

For a standard single-mode fiber, at 1550 nm wavelength, the dispersion coefficient is around

+17 ps/(nm·km).

An illustration of the detected response obtained after propagation through a SSMF fiber

is shown in Fig. 4.4. The transmission response is shown for three different αH−parameter

values. A positive dispersion coefficient of +17 ps/(nm·km) and a link length of 50 km was

used in the calculation, i.e., amounting to a total dispersion of +850 ps/nm.

The detected response features a comb of frequency dips following the relation

f 2m,u Lfiber =

c

2λ2Dλ

[

1 + 2u − 2

πarctan (αH)

]

(4.10)

In Eq. (4.10), fm,u represents the frequency of the ‘u’ -th dip. The appearance of the first null

in the transmission response is obtained by setting the value of u = 0. At this modulation

frequency, the fm component resulting due to the interference between the lower sideband

and the carrier frequency interferes destructively with the fm component resulting due to the

interference between the upper sideband and the carrier frequency. One can observe that

4.2. Small-signal chirp 51

0 5 10 15 20

0.0

0.2

0.4

0.6

0.8

1.0

H = -10+1Nor

mal

ized

respon

se

Modulation frequency [GHz]

(a) Transmission response

-2 -1 0 + 1 + 24

6

8

10

12LSSMF = 50kmD = +17ps/nm/km = 1550nm

Firs

t nul

l [G

Hz]

Small-signal H-parameter

(b) Small-signal transmission limit

Fig. 4.4: Calculated small-signal transmission response of an EML for three different small-signalchirp-parameters. The response was obtained after propagation through a fiber link having apositive dispersion. The comb of dips shifts toward higher frequencies for increasingly negativechirp-parameters.

the first null appears at higher frequencies for increasingly negative chirp-parameter values

(for the case of positive dispersion coefficient assumed). The figure also illustrates that even

a zero chirp-parameter is susceptible to dispersion and suffers a finite transmission limit.

This is a consequence of the interference between the sidebands arising solely due to inten-

sity modulation. In this case, one speaks from Fourier transform-limited pulses. Hence, the

chirp-parameter merely indicates a degradation or an enhancement in the dispersion-limited

transmission. In general, up to a certain extent, the transmission limit can be enhanced if

the product of dispersion coefficient and chirp-parameter is negative and the transmission

limit degrades if the product assumes positive values.

For small-signal chirp characterization, the frequency dips obtained from the response are fit-

ted using Eq. (4.10). The slope of the fit yields the total dispersion (dispersion coefficient×link

length) of the link employed. The intercept of the fit (which depends both on the magnitude

and sign of the dispersion coefficient) yields the small-signal chirp-parameter. The dispersion

coefficient obtained by this method is always positive and hence care should be exercised in

determining the sign of the dispersion coefficient depending upon the type of fiber used. This

is of prime importance because the sign of the deduced chirp-parameter is dependent on the

sign of the dispersion coefficient.

4.2.2 Experimental setup for small-signal chirp measurements

The experimental setup implemented for investigating the small-signal chirp measurement is

shown in Fig. 4.5.


PhotodiodeDispersive link

Ports

Network analyzer

1 2

DUTElectrical

Optical

Device Under Test

Fig. 4.5: Experimental setup implemented for small-signal chirp measurements.

A small electrical signal provided by a network analyzer is applied to the device under test

(DUT) biased at the voltage of interest. The electro-optic small-signal response is collected

and propagated through a dispersive link and finally detected at the network analyzer. In

order to measure reliable small-signal chirp-parameters, the link employed must provide suf-

ficient dispersion. This ensures that at least two frequency dips appear within the range of

measurement bandwidth in order to perform a straight line fit and subsequent parameter

extraction. Finally, the small-signal chirp method can be employed to determine reliable

chirp values in the range of −5 to +5. For chirp-parameters lying well away from this range,

the transmission response shows reduced sensitivity thereby increasing measurement uncer-

tainty. This sensitivity dependence is a result of the ‘arctan’ dependency of the αH-parameter

observed in Eq. (4.10).

In this work, two different fiber types are employed. Standard single-mode fibers (SSMFs) are

used for the investigation of 1550 nm EMLs. Since SSMF show negligible dispersion around

the 1310 nm wavelength regime, dispersion shifted fibers (DSFs) are used for the investigation

of 1310 nm EMLs. The dispersion coefficient of DSF is around −18 ps/(nm·km) near 1310 nm.

4.3 Time-resolved chirp (TRC) measurements

For high-speed communication applications, it becomes necessary to characterize the instan-

taneous frequency deviations occurring within individual pulses, to assess or simulate system

performance. Such methods capable of resolving frequency changes in the time domain are

termed as time-resolved chirp (TRC) measurements.

TRC measurement methods, operating in the time domain, can be mainly classified into two

types. In the first method, a high resolution spectrometer or a grating is scanned over the

4.3. Time-resolved chirp (TRC) measurements 53

time period of interest by step-tuning a filter passband and a wavelength trace for each scan

is recorded. The acquired raw data is then sorted by time to calculate the optical chirp [60].

The method, however, requires long measurement times. In the second approach, the optical

chirp is tracked using interferometer configurations such as Michelson, Mach-Zehnder [61] or

Fabry-Perot (FP) [62]. These methods exploit the frequency dependent transmission prop-

erties of the interferometers to convert frequency variations into power variations. In such

methods, the slope of the interferometer transmission is one of the important design para-

meters to achieve a desired sensitivity (FM-IM sensitivity) for a given bit-rate.

In the case of Michelson and Mach-Zehnder interferometers, the optical path difference be-

tween the two interfering beams can be varied to achieve the desired sensitivity. In the

case of FP based interferometers, the sensitivity can be varied by two design parameters,

namely, the reflectivity of the mirrors (R) and the free spectral range (FSR) of the cavity.

Fabry-Perot resonators offer added advantages in that they are polarization insensitive at

angles close to normal incidence. In this work, an air-cavity based FP resonator, (also called

etalons, when the FSR is fixed) is employed due to the relatively low temperature sensitivity

of air over solid etalon structures.

4.3.1 Principle of measurement

This section describes the principle of the time-resolved chirp measurement method employ-

ing a Fabry-Perot resonator. The resonator specific properties such as mirror reflectivity and

free spectral range and their significance on the measured bit rate will be introduced in the

subsequent sections.

In the following treatment, frequency changes shall be considered rather than wavelength

changes to avoid any confusion while interpreting measurement results. For instance, an

optical wave propagating in a linear medium of refractive index n′ undergoes a change in

wavelength compared to its free space wavelength λ, i.e., λmedium = λ/n′. In contrast, the

frequency of light remains the same. One has to distinguish this phenomenon from light

chirping, where frequency of light itself changes, which apparently results in a wavelength

change. Secondly, the spectral properties of a FP resonator (free spectral range and trans-

mission slope) are independent of the absolute wavelength of light. Thus, expressing in terms

of frequency changes facilitates the usage of consistent expressions over the complete wave-

length window of interest.

The transmission of a FP resonator is periodic with respect to frequency, and repeats itself

over one free spectral range. Fig. 4.6 shows a schematic of the interferometer transmission

characteristic as a function of frequency. For illustration, only frequencies falling within

one free spectral range have been shown. For frequencies falling within the first half of the

free spectral range, the transmission increases as a function of frequency. By contrast, for


frequencies lying above one half of the free spectral range, the transmission decreases as

a function of frequency. This change in power per unit frequency interval is maximum at

the 3 dB points on the transmission curve. The 3 dB points TD are obtained as the average

between the maximum and minimum transmission values, Tmax and Tmin, respectively as

TD =1

2[Tmax + Tmin] (4.11)

The 3 dB points on either side of the transmission are denoted as T+ and T−, respectively as

indicated in Fig. 4.6. This frequency dependent transmission property at the discrimination

points is exploited for resolving light chirping in time domain.

As a first step, the laser wavelength whose chirping behavior is to be characterized is made

to coincide with the positive discrimination point T+. At this point of the interferometer

transmission, an increase in power due to intensity modulation (IM) accompanied by a si-

multaneous increase in frequency, due to frequency modulation (FM) results in a response

proportional to IM+FM. The response of the same pulse, at the opposite discrimination

point T− results in IM-FM.

(IM+FM) (IM-FM)

Tra

nsm

issi

on

Frequency

T+TD

TMIN

TMAX

T-

in

Fig. 4.6: Schematic representation of the interferometer transmission curve. Shown are the positiveand negative discrimination points on either side of the transmission slope.

Fig. 4.7 summarizes the principle of TRC measurement using a FP resonator. A time domain

pulse, whose chirp behavior is unknown, is passed through the resonator with the carrier

frequency locked at the two discrimination points of interest. This results in two different

responses IM+FM and IM-FM. The reduction in average power of the responses is a result

of the 3 dB losses occurring in the transmission.


Time

IM+FM IM-FM

Input IMUnknown FM

Power change

Responses

Fabry-Perot

1

3

2

Deduced FM

Fig. 4.7: Schematic of the principle illustrating the time-resolved chirp measurement method usinga Fabry-Perot resonator. The responses obtained from either sides of the transmission are used tocalculate the frequency chirp of the intensity modulated waveform.

After recording the two responses, the difference in power due to FM is deduced by simply

subtracting the two waveforms, i.e.,

∆PFM =1

2[T+ response − T− response]

=1

2[(IM + FM) − (IM − FM)] (4.12)

The power variation ∆PFM obtained eliminates the contribution due to IM and is proportional

to FM only. The FM power change obtained depends on the following:

• frequency chirp of the input waveform

• transmission slope of the Fabry-Perot resonator

• average power of the input pulse incident on the resonator

• scattering and/or absorption losses of the resonator


The obtained power variation ∆PFM in Eq. (4.12) serves as the input for subsequent calcu-

lation of frequency chirp. The nonlinearity of the transmission and the discrimination point

has to be taken into account for estimating reliable frequency chirp. An expression for the

same is presented in the subsequent sections. The average power due to intensity modulation

alone PIM is the average of the two responses, i.e.,

PIM =1

2[T+ response + T− response]

=1

2[(IM + FM) + (IM − FM)] (4.13)

Thus the power contribution due to the frequency modulation component (FM) cancels out

leaving only the intensity modulation component to be extracted.

4.3.2 Design of Fabry-Perot resonator

As mentioned in the previous section, the obtained power change, apart from other para-

meters, is dependent on the slope of the transmission curve. We shall refer to the slope

as FM-IM sensitivity. Other terms that are widely used in the literature include FM-AM

demodulation coefficient, FM-AM gain coefficient, AM standing for amplitude modulation.

The notation FM-IM was preferred (rather than FM-AM), since IM is a practical quantity

that is measured in experiments.

The resonator should possess an optimal value of FM-IM sensitivity without compromising

the spectral bandwidth of detection. Two parameters of the resonator influence FM-IM

sensitivity and the detection bandwidth, viz.,

• free spectral range

• mirror reflectivity

The optical path length of the cavity determines the free spectral range of the transmission

spectrum. The free spectral range FSR is defined as the frequency separation between two

adjacent maxima [3]

FSR =c

2n′LFP

(4.14)

where LFP is the cavity spacing (mirror separation) of the resonator and n′ the refractive

index. The FSR is inversely proportional to the cavity spacing.

The mirror reflectivity governs the finesse2 F of the resonator. It is related to the mirror

reflectivity R as [2]

2The total finesse F of a resonator, apart from mirror reflectivity R, must include surface roughness andabsorption losses in the resonator. The latter two quantities start dominating and become relevant only forR values > 97% (e.g. spectrometer applications).


F =π√

R

(1 − R)(4.15)

Eq. (4.15) indicates that the finesse factor becomes highly nonlinear for increasing values of R.

For R values close to 1, the (1−R) factor in the denominator tends to zero, and the finesse

approaches infinity. The finesse is a measure of the quality factor of the resonator which

influences the spectral bandwidth of the resonance. The higher the finesse, the narrower is

the spectral bandwidth.

Fabry-Perot sensitivity:

The FM-IM sensitivity |dTFP/dν| at the discrimination point νD (frequency corresponding

to the transmission TD) is given by [62]

∣∣∣∣

dTFP

dν

∣∣∣∣ν=νD

=2π

FSR

[

2R(1 + R2)

(1 + R)2(1 − R2)

]

(4.16)

Qualitatively, it is evident from Fig. 4.6, that the steeper the slope of the transmission, the

larger is the power change (sensitivity) obtained for a given chirp.

Spectral bandwidth:

In Fig. 4.6 the input wavelength λin was assumed to be a narrow linewidth spectrum closely

resembling a δ−function. This is a reasonable assumption for an unmodulated DFB spectrum

since its linewidth is of the order of a few MHz [3]. However, realistic modulated spectrum

is composed of IM and FM sidebands spanning a certain frequency range. This implies that

the complete spectrum encompassing the carrier and the sidebands, has to be superimposed

on either side of the transmission slope. High bit rates and large frequency chirp inevitably

broaden the frequency spectrum. In other words, the spectral width of the resonance emerges

as a critical parameter for characterizing high bit rate sources. The 3 dB bandwidth ∆ν3 dB

of the resonance is a function of both the FSR and the finesse values of the resonator given

by [2]

∆ν3 dB =FSR

F

=

[c

2n′LFP

]/[

π√

R

(1 − R)

]

(4.17)

In Eq. (4.17) the value of the refractive index n′ can be set to unity, since an air-spaced

cavity has been used in this work. The available detection bandwidth on either side of the

transmission is equal to the 3 dB bandwidth.


Fig. 4.8 summarizes the aforementioned considerations by illustrating the IM-FM sensitivity

and the 3 dB optical bandwidth obtained for three different mirror reflectivity values as a

function of the free spectral range.

Choosing a mirror reflectivity of R = 70% and a FSR value of 150 GHz yields an ample

sensitivity of about 6×10−2 GHz−1, whereas the available bandwidth drops to about 20 GHz.

A contradictory behavior can be observed if one chooses a reflectivity of R = 50% and a FSR

value of 600 GHz. The available bandwidth increases but at the expense of the FM-IM

sensitivity which drops below 1× 10−2 GHz−1. From Fig. 4.8, it is apparent that there exists

a clear trade-off between FM-IM sensitivity and the available detection bandwidth.

100 200 300 400 500 6000

1

2

3

4

5

6

7

0

5

10

15

20R = 70%

R = 60%

R = 50%

FM-IM

sen

sitiv

ity [10-2

/GH

z]

Free spectral range [GHz]

Pow

er v

aria

tion

[µW

]

(a) FM-IM sensitivity

100 200 300 400 500 6000

40

80

120

160

R = 70%

R = 60%

R = 50%3 dB

bandw

idth

[GH

z]

Free spectral range [GHz]

(b) 3 dB optical bandwidth

Fig. 4.8: (a) Calculated FM-IM sensitivity (b) 3 dB optical bandwidth for three different mir-ror reflectivity values. A trade-off between sensitivity and available detection bandwidth can beobserved.

In order to illustrate the impact of FM-IM sensitivity on a real measurement, let us assume

an input waveform approximated by a Gaussian envelope. Let the ON and OFF state power

be 1 mW and 100µW (corresponding to an extinction ratio of 10 dB), respectively. Let the

peak chirp encountered be 5 GHz. The left-hand side axis of Fig. 4.8 (a) shows the sensi-

tivity values obtained for several mirror reflectivity values. The corresponding maximum

change in power ∆PFM, at the point of maximum frequency excursion is plotted on the

right-hand side axis of Fig. 4.8 (a). Taking transmission losses of about 3 dB (transmission

at TD ≈ 0.5 × TMAX) into consideration along with a total optical loss of about 7 dB, one

obtains power changes around 6µW, i.e., a factor of ≈ 90 less than the average optical power

at input. This simple calculation shows the stringent power requirements that has to be

coped with, in the absence of any external optical amplification.


In this work, a reflectivity of R = 60% is employed, letting the free spectral range as an in-

dependent parameter that can be tuned to optimize specific measurement requirements. For

instance, for low bit rate measurements (and hence small modulated spectrum bandwidth), if

one encounters low power values and/or low frequency chirp, the sensitivity can be increased

by decreasing the free spectral range (increasing the cavity spacing).

4.3.3 Experimental setup for TRC measurements

The experimental setup implemented for TRC measurements consists of a resonator formed

by an air gap enclosed between two mirrors. Light is coupled in and out of the cavity using

collimators. The mirrors possess a high-reflection (HR) coating of R ≡ RHR = 60% and an

anti-reflection (AR) coating RAR < 0.1% on the inner and the outer walls, respectively as

shown in Fig. 4.9.

Inputcollimator

Outputcollimator

Fabry-Perot

SMFSMF

Electrical

Optical

Piezocontrolunit

Opticalinput

Opticaloutput

AR coating

R = 60%

Air cavity

M1 M2

Voltagesource

Fig. 4.9: Experimental setup realized for time-resolved chirp measurement of EMLs using anair-cavity based Fabry-Perot resonator.


The two coatings are broad band in nature encompassing the wavelength region between

1280 nm and 1600 nm. The coupling optics and the collimators used are also capable of

working over the mentioned wavelength range. The focal length of the collimators can be

tuned in order to guarantee paraxial beam operation depending on the wavelength under

consideration. This ensures low loss operation of the setup. The collimators are mounted on

piezoelectric stages capable of performing three dimensional linear translations. In addition,

adjustable angle mounts with an angular resolution of ≈ 0.03 aid in tuning the beam along

the optical axis. Using two successive measurements, the Fabry-Perot response is collected

using an output collimator into a single-mode fiber, by tuning the setup such that λDFB

coincides with the two discrimination points of interest.

Finally, the frequency chirp is calculated using the relation [62]

∆ν(t) ∼= FSR

2πarctan

[(∆PFM

P IM

)

KFP

]

, where (4.18)

KFP =

[TD(1 + R2) − (1 − R)2] − TD(1 + R2)

(1 − R)[(1 − TD)[TD(1 + R)2 − (1 − R)2]

]1/2

(4.19)

is a resonator specific constant that accounts for the nonlinear transmission and the discrim-

ination point [62].

Characterization of Fabry-Perot resonator:

After building the TRC setup shown in Fig. 4.9, it was characterized to extract the trans-

mission properties.

The experimental transmission spectra obtained using a commercial tunable laser source are

shown in Fig. 4.10(a). The contrast of the transmission response corresponds to the reflectiv-

ity of the mirrors employed, implying that there are negligible scattering and/or absorption

losses within the cavity. The first derivative of the transmission with respect to optical fre-

quency yields the frequency modulation to intensity modulation (FM-IM) sensitivity. A plot

of the FM-IM sensitivity is shown in Fig. 4.10(b).

After performing a fit to the familiar Airy function, a free spectral range of 266 GHz (≈ 1.52 nm

at 1310 nm) corresponding to a cavity spacing of 564µm and a FM-IM sensitivity of 0.022/GHz

was extracted (at the 3 dB discrimination points of interest).


0.0

0.2

0.4

0.6

0.8

1.0

1310 1309 1308 1307 1306 1305

-399 -266 -133 0 133 266 399

FSR = 266 GHz

Wavelength [nm]

Nor

m. t

rans

mis

sion

Relative frequency [GHz]

(a) Transmission

-4

-2

0

2

4

1310 1309 1308 1307 1306 1305

-399 -266 -133 0 133 266 399

FSR = 266 GHz

Wavelength [nm]

FM-IM

sen

sitiv

ity [1

0-2/G

Hz]


(b) Transmission derivative

Fig. 4.10: (a) Experimental transmission response of the realized Fabry-Perot structure obtainedusing a commercial tunable laser source. A free spectral range of 266 GHz corresponding to acavity length of 564µm is obtained (b) calculated derivative of the transmission spectrum. Afrequency modulation to intensity modulation (FM-IM) sensitivity of 0.022/GHz is obtained at thediscrimination points of interest.

Tuning the cavity spacing:

The schematic in Fig. 4.6 illustrated TRC measurement by tuning the input wavelength

at the opposite slopes of the transmission. However, while performing measurements, the

emission wavelength of the transmitter remains fixed. Therefore, the resonator transmission

has to be tuned so as to get the emission wavelength at the discrimination points of interest.

This is achieved by varying the cavity spacing by way of piezoelectric transducer tuning.

The piezoelectric elements are mounted symmetrically onto one of the mirror holders. A

DC voltage is fed to a ramp amplifier that is set to deliver a fixed voltage gain of 100. By

varying the voltage applied to the piezoelements, the round trip phase condition for the differ-

ent wavelengths can be varied. This effectively results in a shift of the transmission spectrum.

Fig. 4.11 shows the experimental voltage tuning characteristics of the resonator. The wave-

length of input light (CW) provided by a commercial tunable laser was kept fixed at 1310 nm.

(The absolute wavelength does not influence the tuning properties of the resonator). As the

voltage applied to the piezoelectric transducers increases, the cavity length becomes shorter.

This results in a blue-shift of the resonances according to the relation:

∆ν

ν= −

(∆LFP

LFP

)

(4.20)

The shift of the resonance in Eq. (4.20) is purely a function of the resonator length. The

positive and negative discrimination points are indicated in the experimental transmission as


0 100 200 300 400 500 600 700 8000.0

0.2

0.4

0.6

0.8

1.0

T+ T-

in = 1310 nm

Nor

m. t

rans

mis

sion

External voltage [V]

Fig. 4.11: Normalized transmission of theFabry-Perot cavity measured for a fixed in-put wavelength of λin = 1310 nm. Thetransmission varies as the piezo-voltage isvaried. Shown are the positive and the nega-tive discrimination points used for TRC mea-surements.

a function of external voltage. The discrimination point T+ lies where the transmission de-

creases with applied voltage. Since the resonant wavelength blue-shifts with applied voltage,

T+ guarantees positive transmission slope with respect to frequency.

4.3.4 Phase distortion in Fabry-Perot resonators

In the previous sections, the frequency dependent intensity transmission of the resonator

was discussed. This property was qualitatively shown to be exploited for TRC measure-

ments. Besides its frequency dependent transmission, the resonator stores maximum field

energy for the resonance frequencies. The field energy decreases as one moves away from the

peak transmission (off-resonance frequencies). The result is a nonlinear phase contribution

of the resonator, its magnitude and sign depending upon the frequency detuning from the

resonance peak. In effect, on an average, the resonant photons spend more time within the

cavity (cavity life-time) and the off-resonant photons spend comparatively less time. This

adds uncertainty in TRC measurements, since different frequencies arrive at the detector at

different time intervals due to the nonlinear phase response of the Fabry-Perot resonator.

This section describes the effect of phase distortion on the measured responses. Calculated

values for the frequency transfer function of the resonator are presented. The calculation is

validated by means of measurement results. Subsequently, the effect of cavity life-time on

a narrow input spectrum is presented. Finally, a measured modulated spectrum is used to

demonstrate the measurement uncertainty involved.

Fig. 4.12 shows the calculated magnitude response and phase response of the cavity over a

cavity round trip phase of 2π (corresponding to one free spectral range). The magnitude

response, also called the amplitude transfer function, is the square root of the intensity

transfer function observed in an experiment (e.g. Fig. 4.10(a)).


0.0

0.2

0.4

0.6

0.8

1.0

-1.0

-0.5

0.0

0.5

1.0

(p+1)2p(2 )

arg [H( )]

|H( )|

Mag

nitu

de re

spon

se

Round trip phase Ph

ase

resp

onse

[rad

ians

]

Fig. 4.12: Calculated magnitude and phase re-sponse of a Fabry-Perot over a cavity round tripphase of 2π, where ‘p’ is an integer.

Fig. 4.13 (a) shows the calculated and measured cavity life-time and Fig. 4.13 (b) the calcu-

lated and measured cavity dispersion as a function of relative frequency. The measurement

was performed using the phase shift method [53, 63]. For a cavity length of LFP = 564µm

(which corresponds to the experimental spectra obtained in Sect. 4.3.3), the cavity life-time

is spread over a range of approximately 7.2 ps. The small undulations observed close to

the minima are a result of very low Fabry-Perot transmission which eventually limits the

detected phase stability.

-300 -200 -100 0 100 200 300

0

2

4

6

8

10LFP = 564µm

Cav

ity li

fe-ti

me

[ps]


(a) Cavity life-time

-300 -200 -100 0 100 200 300-0.4

-0.2

0.0

0.2

0.4

45

30

15

0

-15

-30

-45LFP = 564µm

Cav

ity d

ispe

rsio

n [p

s/G

Hz]


[ps/

nm]

(b) Cavity dispersion

Fig. 4.13: Experimental (solid circles) and calculated (line) (a) cavity life-time and (b) cavitydispersion of the Fabry-Perot corresponding to the transmission shown in Fig. 4.10(a).

The cavity dispersion (in terms of frequency) is obtained by differentiating the cavity life-

time with respect to optical frequency. (For easy interpretation, cavity dispersion in terms

of wavelength is plotted on the right-hand side.) It is a convenient measure to visualize

the effect of pulse distortion. The cavity dispersion values on the opposite slopes have the

same magnitude but differ in their signs. The maximum cavity dispersion values occur at


the positive and negative discrimination points of interest ≈+0.2 ps/GHz and −0.2 ps/GHz,

respectively. The small ripples in Fig. 4.13 (b) are a result of the undulations observed in the

cavity life-time curve presented in Fig. 4.13 (a).

The cavity dispersion has important implications while performing TRC measurements. As

an illustration, consider a hypothetical waveform having a positive chirp of around 6 GHz

being examined by the Fabry-Perot resonator. For visualization, the wave is assumed to

have a narrow spectrum as was shown in Fig. 4.6. Fig. 4.14 schematically summarizes the

observation.

Discrimination point T+ : At T+, the positive frequency excursion during cycle ‘2’ ex-

periences large cavity life-time shown as 2+ and the negative frequency excursion cycle ‘4’

experiences small cavity life-time shown as 4+. The net effect upon detection at the sam-

pling scope is sketched in Fig. 4.14 (c). The photons (and thereby their power contribution)

corresponding to 2+ is delayed with respect to cycles ‘1, 3 & 5’. In contrary, the photons

corresponding to 4+ arrive earlier in comparison to cycles ‘1, 3 & 5’.

Discrimination point T− : At T−, the positive frequency excursion during cycle ‘2’ ex-

periences small cavity life-time shown as 2− and the negative frequency excursion cycle ‘4’

experiences large cavity life-time shown as 4−. The net effect of T− discrimination point upon

detection is also included in Fig. 4.14 (c). The photons (and thereby their power contribu-

tion) corresponding to 2− arrive earlier and 4− delayed by a certain amount in comparison

to cycles ‘1, 3 & 5’.

The measurement procedure for frequency chirp extraction was qualitatively described in

Sect. 4.3.1 where the power difference due to FM was obtained by subtracting the power val-

ues at each and every time point of the corresponding two responses. Thus, the magnitude

of power at any instant of time has a profound influence on the frequency chirp extracted.

In other words, the resonator dispersion adds a systematic frequency dependent timing jitter

adding uncertainty to the measured chirp.

The outcome of early or delayed arrival of photons on the responses is sketched in Fig. 4.15 (b).

A waveform similar to the one sketched in Fig. 4.14 (a) was used as input, i.e., with a posi-

tive frequency chirp. We notice that at any specific point of time, the absolute power values

have been dramatically altered. The specific distortion profile is highly dependent on the

transmission properties of the Fabry-Perot resonator and the accompanying chirp. Without

dispersion effects, photons of all frequencies experience identical delay times and therefore

a linear relationship results in Fig. 4.14 (c). The resulting ideal responses are shown in

Fig. 4.15 (a).


Time

Input IM

Accompanying FM

1

2

3

4

5

1 2 3 4 5

1

(a) Input pulseC

avit

y l

ife-

tim

e

Frequency

T+ T-

in

1,3,5 1,3,5

2+

4+

4-

2-

(b) Cavity life-time

0 5 10 15 20 250

5

10

15

20

25

30

4-

2-

4+3

5

2+

1

Offset due to cavity lifetimeat the discrimination point

T-

T+

Freq

uenc

y de

pend

ent

time

dela

y [a

rb. u

nits

]

Time [arb. units]

(c) Effect of cavity dispersion on optical detection

Fig. 4.14: Illustration of the effect of cavity life-time on the waveforms captured on the oppositeslopes of the transmission. (a) Input pulse accompanied by frequency modulation (b) cavity life-time for different regions of the pulse (c) effect of cavity dispersion on optical detection at a samplingscope.

In the above illustration, the input wavelength was assumed to resemble a δ-function. How-

ever, as mentioned earlier, intensity modulated light features spectral components around

the carrier. An example of such a spectra superimposed on the transmission spectrum of the

Fabry-Perot is shown in Fig. 4.16.


0 5 10 15 20 25 30 35

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

T- T+

Pow

er [a

rb. u

nits

]

Time [arb. units]

(a) Ideal responses

0 5 10 15 20 25 30 35

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7T- T+

Discr. point time offset

Power contribution arrives after delayPower contribution

arrives earlier

Pow

er [a

rb. u

nits

]

Time [arb. units]

(b) Distorted responses

Fig. 4.15: Calculated (a) ideal responses without cavity dispersion effects (b) distorted responseswith cavity dispersion effects for the schematic waveform shown in Fig. 4.14 (a).

-150 -100 -50 0 50 100 150

0.0

0.2

0.4

0.6

0.8

1.0Discriminationpoint 2

Discriminationpoint 1

T-T+

Tran

smis

sion


Fig. 4.16: Schematic illustration of a modulated spectrum superimposed on the transmissionspectrum of a Fabry-Perot resonator. The discrimination points of interest are also indicated withthe carrier frequency locked at one of the discrimination points.

The discrimination points of interest are also indicated with the carrier frequency locked

at one of the discrimination points. After transmission through the resonator, each of the

spectral component experiences different delay times thereby reaching the sampling scope at

different time intervals. Hence, the power detected at any instant of time is the contribution

of photons in adjacent time slots arriving at the scope. This makes the calibration procedure

cumbersome to be performed in the time domain. An elegant way is to exploit the frequency

domain properties by way of a Fourier transformation.


Frequency domain analysis:

For calculations, power waveforms directly detected at an oscilloscope (without Fabry-Perot)

were Fourier transformed using a FFT (fast Fourier transform) algorithm. The obtained

Fourier coefficients were multiplied with the amplitude and phase factors (Fig. 4.12) of the

Fabry-Perot in the frequency domain (cf. Appendix C).

0 100 200 300 400 500 600-10

-5

0

5

10systematic error due to cavity dispersionDUT chirp

Chi

rp [G

Hz]

Time [ps]

Fig. 4.17: Illustration of the effect of dispersion on the measured frequency chirp. Device undertest (DUT) chirp is indicated by a line and the calculated chirp with dispersion effects is indicatedby dots.

Since the Fabry-Perot resonator belongs to the class of multi-passband filters, its transmis-

sion repeats over a free spectral range. Thus, the transmission value at a frequency is not

unique (as compared to a low-pass filter, for instance). Hence care was exercised to get

the carrier frequency at the discrimination points while performing FFT. The resulting fre-

quency spectrum was then used to reconstruct the wave in the time domain by performing

an inverse fast Fourier transformation (IFFT). The results of the influence of dispersion on

the measured frequency chirp are shown in Fig. 4.17. The chirp of the DUT is indicated by

a solid line and the calculated chirp with dispersion effects is indicated by dots. Clearly, a

considerable distortion can be observed due to dispersion effects.

4.3.5 TRC measurement considerations

In the previous section, the systematic measurement uncertainty introduced by a Fabry-Perot

resonator was presented. In the following, the effect of rather unpredictable or random errors

on the measured frequency chirp is presented.


Device under test (DUT) stability:

One of the prime requirements for high-speed TRC measurements is a stable single-mode

operation of the investigated devices. Any disturbance that might affect the spectral behavior

of the longitudinal mode will inevitably give rise to measurement uncertainty or even end up

in unreliable results. For instance, an internal disturbance might be caused due to residual

optical reflection at the facet, for very strong pump levels of the laser or the integrated

amplifier. An optical switch was included in the optical path of the setup to monitor the

wavelength stability during the measurements.

Setup stability:

Since frequency changes are converted into power variations, the total loss of the optical path

must be constant over the two consecutive measurements. For instance, the optical coupling

efficiency of the fiber must be identical between the two measurements.

The stability of the resonator and the accompanying optics has to be guaranteed to avoid

drift of the transmission (from the discrimination points). For this purpose, the cavity was

insulated from ambient air drifts.

Finally, external factors might interfere with the spectral behavior. This, for instance, in-

cludes temperature and/or air drifts. Since the DFB wavelength is sensitive to temperature,

e.g. wavelength shifts by ≈ 0.115 nm/K (nanometer per Kelvin) at 1310 nm, the device has to

be temperature stabilized to better than ±0.05C. A 0.25C mean temperature change will

result in a shift of the discrimination point by about ≈ 5 GHz. This shift in the wavelength

appears as an adiabatic component in the measurement.

As an illustration, the effect of 5 GHz drift at the positive discrimination point of the trans-

mission is presented in Fig. 4.18. The origin of the drift can be either due to the DUT

itself (spectral shift) or the experimental setup (temperature drift) as mentioned above. The

assumed input chirp is positive with a peak value of about 9 GHz.

A +5 GHz change along the positive slope of the curve (T+) increases the adiabatic component

considerably while simultaneously providing an underestimate of the transient chirp along

the rising edge. Similarly, a −5 GHz change along the positive slope of the curve results in a

negative adiabatic component while simultaneously underestimating the transient chirp along

the falling edge. Thus, the specific profile of the chirp waveform is considerably influenced by

the accuracy with which the emission wavelength can be locked at the discrimination points.

Smoothing:

The responses captured at the oscilloscope are usually averaged to enhance the signal to

noise ratio (SNR). Whereas this is beneficial during the measurements, smoothing the pulse


0 5 10 15 20 25-15

-10

-5

0

5

10

15

-5GHz change

+5GHz change

Perfect coincidence

Chi

rp [G

Hz]

Time [arb. units]

Fig. 4.18: Effect of drift of lasing frequency or mean temperature change on the measured time-resolved chirp. For illustration purposes, the frequency change (i.e., deviation from discriminationpoint) was assumed to occur for operation at the positive discrimination point only. For comparison,frequency chirp measured for perfect coincidence with the discrimination points is also included(dotted line).

waveforms externally (e.g. software processing after measurements) to enhance SNR is crit-

ical for high-speed TRC interpretation. This is because, smoothing invariably reduces the

steepness of rise and fall times. (In the jargon of signal processing, the smoothing operation

is the implementation of a moving average filter.) As noted previously, the power values at

each and every time point are decisive for TRC extraction.

4.3.6 Estimation of effective chirp-parameter

One of the prime objectives of TRC measurements is to extract an effective chirp-parameter

αH−eff which is representative of the measured profile and that is capable of adequately de-

scribing the signal transmission along a link.

The small-signal chirp analysis introduced earlier in this chapter is useful for extracting the

chirp-parameter around a given EAM bias. However, it is strongly dependent upon the bias

voltage. Several different approaches have been reported in the literature for the extraction

of an effective large-signal chirp-parameter. For instance, average chirp values have been

reported based on the chirp data encountered between the ‘ON’ and ‘OFF’ states [64] or

between the ‘ON’ state and the 3 dB transmission [30]. Indeed, αH−eff has been reported to

be correlated with the ratio of the phase change to the loss change between the ‘ON’ state

voltage and the voltage at which the excitonic peak reaches the wavelength of light source [65].


These approaches, however, seem to be more structure specific since for identical excitonic

peak wavelengths, the chirp-parameter could be very different depending on the wavelength

of operation as discussed in Sect. 3.9. An unambiguous method, however, is to iteratively

force to match an assumed chirp-parameter with the measured TRC data as reported for

instance in Ref. [66].

4.4 Impact of chirp on system performance

The maximum ‘bit rate-square root fiber length product’ BR

√Lfiber that can be achieved in

an optical communication system is dependent on the sign and magnitudes of the effective

chirp-parameter αH−eff of the transmitter and the dispersion coefficient of the fiber. This is

schematically illustrated [9] for pulse propagation in an optical fiber possessing a positive

dispersion coefficient (anomalous dispersion regime).

Effective chirp-parameter

-5 0 +5

Zero chirpSlight negative chirp

Positive dispersioncoefficient of fiber

BR

Lfi

ber

Fig. 4.19: Schematic representation of maximum ‘bit rate-square root fiber length product’ as afunction of effective chirp-parameter [9] for pulse propagation in the anomalous dispersion regime(positive fiber dispersion coefficient).

For positive αH−eff , propagation in the anomalous dispersion regime is limited by vertical eye

closure penalty. This is a consequence of the bits starting to spread out of the allotted time

slot right from the start of propagation in the fiber. Up to some extent, the transmission

limitation can be overcome by external amplification thereby increasing the signal to noise

ratio. This external amplification needed for compensating the effects of inter symbol inter-

ference (ISI) is referred to as dispersion power penalty.

A negatively chirped pulse propagating in the anomalous dispersion regime of the fiber un-

dergoes pulse compression till it reaches its Fourier-transform limited pulse width. At this

point, the pulse spectrum is completely deprived of spectral chirp (i.e., the effective chirp

4.4. Impact of chirp on system performance 71

becomes zero). Thereafter, fiber dispersion results in pulse broadening. This illustrates that

a slight effective negative chirp-parameter αH−eff ≈ −0.5 is beneficial to extend the trans-

mission distance (in the assumed positive dispersion coefficient) beyond the dispersion limit,

i.e., BR

√Lfiber that can be achieved with a zero-chirp transmitter.

However, for very high effective negative chirp-parameters, say αH−eff less than −1, the trans-

mission limitation arises due to jitter penalty [30]. Physically, the narrow ‘ones’ (bit ‘1’) start

to broaden before the wider ‘ones’ have attained their Fourier transform-limited pulse width.

Chapter 5

Experimental Setup for DynamicCharacterization

The experimental setup for dynamic characterization is depicted in Fig. 5.1. A sinusoidal

generator provides the clock frequency to a pseudo-random binary sequence (PRBS) gener-

ator whose sequence length is 211 − 1 (or 27 − 1). The PRBS pattern is then amplified by a

low-noise broad band radio frequency (RF) amplifier and fed into a Ground-Signal-Ground

(GSG) microwave probe through a symmetrical resistive power divider and a bias-Tee with

the appropriate EAM bias. The power divider monitors the electrical reference at a wide

bandwidth oscilloscope which is triggered by the PRBS generator. The microwave signal

traveling along the modulator is terminated by a 50 Ω resistor RL, to improve RF matching.

5.1 Large-signal characterization

For performing large-signal modulation experiments, modulated light output from the facet

is collected using a lensed fiber. The signal is then directly detected (detouring the TRC

setup) by a high-speed photodiode. The resulting electrical waveform is fed to the oscillo-

scope. Delay between the detected signal and the electrical trigger signal is compensated by

adjusting the delay time at the scope. Optical waveforms or correspondingly eye diagrams

can be displayed at the oscilloscope.

5.2 Time-resolved chirp characterization

Modulated light output from the facet is collected using a lensed fiber and collimated into a

paraxial beam which then enters the FP cavity. Using two successive measurements, the cav-

ity response is collected using an output collimator into a single-mode mode fiber, by tuning

the setup and let the laser emission wavelength λDFB, coincide at the discrimination points.

Finally, the waveforms are detected by the photodiode and displayed at the oscilloscope.

The EML chip is temperature stabilized to better than ±0.05 C to guarantee wavelength

stability during the measurements. The total insertion loss of the optical path is around 4 dB

72

5.2. Time-resolved chirp characterization 73

Oscilloscope

Electricalreference

Tri

gg

er

Bias-Tee

SMF

Piezocontrol

Inputcollimator

Outputcollimator Fabry-Perot

SMF

6dB

1 mW

Opticalspectrumanalyzer

Opticalpowermeter

Photodiode

PRBSgenerator

Sinusgenerator

Clock211 -1

DUT

DC block

Lensedfiber

ILD

RL

Temperaturecontrol

Op

tica

l si

gn

al

RFamplifier

GSGProbe

VEAM

6dB

Powerdivider

ElectricalOptical

Fig. 5.1: Experimental setup realized for dynamic characterization of EMLs and EML-SOAs. Largesignal modulation experiments are performed by detouring the TRC setup and directly detectingthe signal at the oscilloscope. Time-resolved chirp measurements are performed using the completesetup. The setup is capable of operating over a wide wavelength range of 1280–1600 nm.

and the setup is capable of operating over a wide wavelength range of 1280–1600 nm owing

to its broad band mirror coating and the optics used.

Lithium-Niobate modulator as DUT

The realized TRC setup was tested using a commercial dual-drive Mach-Zehnder modulator

(MZM) capable of modulating up to 10 Gbps. A continuous wave (CW) input to the MZ

modulator was provided by a commercial tunable laser source. The wavelength of the input

light was 1550 nm. The polarization maintaining input at the MZM was directly connected

to the tunable laser source.

74 Chapter 5. Experimental Setup for Dynamic Characterization

The modulation signal was generated using the electrical setup shown in Fig. 5.1. One of

the arms of the modulator was modulated by a simple ‘101010. . .’ NRZ sequence at 10 Gbps

with the other arm grounded. A peak-to-peak modulation voltage of 3.3 V was applied

with the DC bias maintained at −1.9 V. An erbium-doped fiber amplifier was used for pre-

amplification to increase the signal to noise ratio at the scope.

0 50 100 150 2000.0

0.2

0.4

0.6

0.8

1.0

Response at T+

Response at T-

Nor

mal

ized

resp

onse

Time [ps]

(a) Calculated responses

0 50 100 150 2000.0

0.2

0.4

0.6

0.8

1.0

Response at T-

Response at T+

Nor

mal

ized

resp

onse

Time [ps]

(b) Experimental responses

Fig. 5.2: (a) Calculated and (b) experimental responses obtained after passing the modulatedspectrum of a commercial MZ modulator through TRC setup with the carrier frequency locked atthe discrimination points. For the calculations, a peak chirp of 6 GHz was assumed. A ‘101010. . .’NRZ sequence at 10 Gbps was used for modulation.

Fig. 5.2 compares the calculated and experimental responses of the MZM at 10 Gbps. The

bit period corresponds to 100 ps in each case. For the calculations, a peak chirp of 6 GHz was

assumed1. The assumed frequency chirp in the time domain can be equivalently represented

by a frequency spectrum through a Fourier transformation (cf. Appendix C).

The calculated responses shown in Fig. 5.2 (a) do not include the transfer function of the

photodiode used for detection. The calculations are still justified, since the photodiode band-

width used for signal detection is ≈ 50 GHz, which is much larger than the data rate used for

measurement. Slight deviations observed between the calculated and the experimental re-

sponses close to the ‘ON’ state are a result of the spectral leakage of the Fourier transformed

spectrum arising from the finite noise level of the captured time domain signal. From the

calculated responses, which includes the effect of Fabry-Perot dispersion, the corresponding

1For the case of positive chirp encountered during the measurements, one can observe from Fig. 4.17, thatthe amplitude of the frequency chirp (i.e., half the value of peak to peak chirp) remains almost unalteredduring the fall time of the pulse. Thus the amplitude of the chirp during the fall time of the pulse was usedas a clue for the calculations.

5.2. Time-resolved chirp characterization 75

0 100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0

1.2

-8

-4

0

4

8

Nor

mal

ized

pow

er

Time [ps] C

hirp

[GH

z](a) Calculated chirp waveform

0 100 200 300 4000

200

400

600

800

-8

-4

0

4

8V bias = -1.9V Vpp = 3.3V

Lithium Niobate MZM

Pow

er [µ

W]

Time [ps]

Chi

rp [G

Hz]

(b) Experimental chirp waveform

Fig. 5.3: (a) Calculated and (b) experimental chirp waveforms of the commercial MZ modulator at10 Gbps. The frequency chirp was calculated from the responses shown in Fig. 5.2. As a reference,the power waveform is also included.

frequency chirp was extracted.

The calculated and experimental frequency chirp waveforms are presented in Fig. 5.3. For

easy reference, the normalized power waveform is also included. The MZM shows a peak

positive chirp of nearly 4 GHz which is an underestimate of the assumed 6 GHz and a peak

negative chirp of slightly more than 6 GHz. This systematic measurement error due to

Fabry-Perot cavity dispersion is clearly observed in both the calculated and measured ones

corroborating the effect of cavity dispersion presented in the previous chapter.

Thus, if the systematic measurement uncertainty introduced by the Fabry-Perot resonator

is known, one can recalculate the undistorted waveforms in the time domain (cf. Appen-

dix C). This result shall be used for the time-resolved chirp investigations presented in the

forthcoming chapters.

Chapter 6

1310 nm Electroabsorption ModulatedLasers

Electroabsorption modulated lasers operating in the 1310 nm wavelength window have the

potential to address the market needs up to 40 km. The primary advantage of exploiting

the 1310 nm wavelength window is the low dispersion of standard single-mode fibers in the

vicinity of 1310 nm. As of today, the maximum transmission distance is recommended up to

40 km since, among other factors, fiber loss dominates the transmission link. Typical fiber

attenuation is around 0.5 dB/km which translates to 20 dB optical attenuation at the receiver

end. This simple estimation of total optical loss shows that the communication systems op-

erating in the 1310 nm wavelength window are primarily loss-limited.

This chapter presents the experimental results of EMLs emitting in the 1310 nm wavelength

window. The 1310 nm EMLs feature a multiple quantum well active layer with 10×5 nm thick

single type QWs whose photoluminescence wavelength (λPL) is 1285 nm at room temperature.

The thickness of the intrinsic area is 300 nm. The operating wavelength of the device is near

1310 nm.

6.1 Static characteristics

Fiber-coupled optical power, static light extinction and the spectral behavior are chosen to

represent the static performance of the device.

Light-current characteristics

Fig. 6.1 (a) shows the experimental light-current characteristics of a 1310 nm EML in contin-

uous wave (CW) operation for various EAM reverse bias voltages. The DFB laser and EAM

sections of the investigated EML are 370µm and 130µm long, respectively.

A heat-sink temperature of 15C was chosen to provide sufficient gain and absorption change

in the laser and modulator sections, respectively. The low temperature operation increases

76

6.1. Static characteristics 77

0 20 40 60 80 1000

250

500

750

1000

1250

-2V

-1V

0VT=15°Ccw operation

Pow

er in

fibe

r [µW

]

Laser current [mA]

|VEAM|

EAM reverse bias voltagevaried in steps of 0.5V

(a) L − I characteristics

0 20 40 60 80 1000

3

6

9

12

15-2V

-1V

0V

T=15°Ccw operation

EAM

pho

tocu

rren

t [m

A]

Laser current [mA]

|VEAM|


(b) EAM photocurrent

Fig. 6.1: (a) Experimental light-current characteristics of a 1310 nm EML in continuous waveoperation for various EAM reverse bias voltages. A heat-sink temperature of 15C was chosen toprovide sufficient gain and absorption change in the laser and modulator sections, respectively. Lightextinction can be observed for increasing EAM reverse bias (b) corresponding photocurrent detectedin the EAM section. DFB laser and EAM sections are 370µm and 130µm long, respectively.

the effective detuning of the operation wavelength. This ensures reduced insertion loss and

optimum extinction values. Light extinction can be observed for increasing EAM reverse

bias. The slight nonlinearities observed in the L − I characteristics are attributed to the

residual optical reflection at the EAM facet which causes marginal instabilities in the lasing

mode. The effect of residual facet reflection becomes progressively less severe for increasing

EAM reverse bias and the modal instability almost ceases to exist at −2.5 V, where much of

the light is being absorbed in the EAM section.

The corresponding photocurrent detected in the EAM section shown in Fig. 6.1 (b) validates

this argument. The detected photocurrent also shows slight nonlinearities at low reverse

bias voltages, whereas it is almost linear at −2.5 V. A maximum fiber-coupled optical power

(coupling efficiency ηc ≈ 40%) of around 1.1 mW (+0.4 dBm) is obtained at 0 V EAM bias.

Extinction and spectral characteristics

Fig. 6.2 shows the static extinction behavior at a laser current of 85 mA. Light extinction of

nearly 18 dB for a voltage swing between 0 V and −3 V can be inferred from the plot. The

corresponding spectrum at a laser current of 85 mA and for an EAM bias of 0 V is shown

Fig. 6.3. The lasing mode around 1309 nm with a side mode suppression ratio (SMSR) of

45 dB can be observed from the plot.

78 Chapter 6. 1310 nm Electroabsorption Modulated Lasers

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.00

5

10

15

20ILD = 85mAT = 15°C

= 1309nm

Extin

ctio

n [d

B]

EAM bias [V]

Fig. 6.2: Experimental static light extinc-tion characteristics of the EML at a heat-sink temperature of 15C, the laser biased at85 mA. Light extinction of up to 18 dB canbe observed for a voltage swing of 3 V.

1304 1306 1308 1310 1312 1314

-70

-60

-50

-40

-30

-20

-10

0ILD = 85 mAVEAM = 0VT = 15°C

> 45 dB

Pow

er [d

Bm]

Wavelength [nm]

Fig. 6.3: Measured optical spectrum show-ing a lasing wavelength around 1309 nm ata temperature of 15 C, the laser biased at85 mA and the modulator at 0V. A SMSR of45 dB is obtained.

6.2 Electrical characteristics

Before performing dynamic optical measurements, the electrical properties of the electroab-

sorption modulators were studied. Electrical investigations render useful information such

as EAM capacitance, electrical input match and electrical transmission characteristics. A

schematic of the equivalent circuit of an EAM integrated into a 50 Ω environment is shown

in Fig. 6.4.

50W R = 16EAM W

R = 50L W

CEAM

Signalsource

Z = 500 W

Microwavetransmission line

Fig. 6.4: Equivalent circuit of an electroabsorption modulator integrated into a 50 Ω environment.The series resistance of the EAM ridge is 16 Ω. The EAM is terminated by a 50 Ω load.

The signal is fed through microwave transmission lines whose line impedance Z0 is 50 Ω. The

series resistance of the EAM ridge (corresponding to an EAM of length 130µm) extracted

from measurements is 16 Ω. The EAM is terminated by a matching resistor RL of 50 Ω.

6.2. Electrical characteristics 79

Extraction of EAM capacitance

The capacitance of the EAM can be estimated using the EAM dimensions and the intrinsic

area thickness:

CEAM = ǫ0ǫrAEAM

dpin

(6.1)

where dpin is the intrinsic area thickness, AEAM = LEAM×Wridge is the EAM area contributing

to capacitance and ǫ0 and ǫr the permittivity of free space and relative permittivity, respec-

tively. With LEAM = 130µm, Wridge = 2.2 µm, dpin = 270 nm and ǫr = 16, the estimated

capacitance is ≈ 0.15 pF.

A traveling wave electrode can be considered as a lumped element electrode, if the electrical

wavelength in the medium (traveling wave electrode) satisfies the condition LEAM < λRF/20.

This condition corresponds to an EAM length of 0.05 with respect to λRF. As an example,

corresponding to a frequency of 1 GHz, the wavelength λRF of the electrical wave in the elec-

trode is ca. 75 mm. An EAM of length 150µm corresponds to 0.002×λRF. The capacitance

contribution of the feed lines can be ignored since a semi-insulating substrate was used. Thus

at 1 GHz, the electric field along the length of the EAM can be treated practically constant

or equivalently the EAM can be considered as a parallel plate capacitor. This enables the

extraction of EAM capacitance from the impedance measurements.

0.2 0.5 1 2 5

-0.2i

0.2i

-0.5i

0.5i

-1.0i

1.0i

-2.0i

2.0i

-5.0i

5.0i

-1V-2V

40 GHz

30 GHz

10 GHz

20 GHz

0V

Laser off

0

Normalized to 50

(a) Smith chart

-2.0 -1.5 -1.0 -0.5 0.00.16

0.18

0.20

0.22

0.24

Laser off

Cap

acita

nce

[pF]

EAM bias [V]

(b) Extracted EAM capacitance

Fig. 6.5: (a) Impedance measurement of an open traveling wave electrode for three different EAMbias voltages (b) extracted EAM capacitance in the absence of light.

The EAM capacitance CEAM can be extracted from the complex impedance Z = R + iX

where R and X represent the resistance and reactance, respectively.


CEAM,meas =1

2πfmodX(6.2)

where fmod is the modulation frequency. The extracted capacitance values in the absence of

light and thus without carriers in the EAM section are plotted in Fig. 6.5 (b). Capacitance

values of about 0.23 pF and 0.19 pF are obtained for EAM bias values of 0 V and −1 V, re-

spectively.

A simple estimate of the modulation bandwidth can be obtained by considering the EAM as

a lumped element as follows:

f3dBe =1

πRCEAM

(6.3)

where R is the total resistance and CEAM the capacitance of the EAM section. The total

resistance R = REAM + (50 Ω ‖ 50 Ω) = 41 Ω yields ≈ 37 GHz (in the absence of light) with

REAM = 16 Ω and CEAM = 0.21 pF. The final modulation bandwidth, however, is also depen-

dent on other parameters such as impedance matching over the frequency range of interest

and the final EAM capacitance in the presence of light [34].

Input match S11

The electrical reflection coefficient S11 of the EAM obtained by terminating the traveling

wave electrode with a 50 Ω resistor gives a measure of the input impedance matching in

the 50 Ω environment. Fig. 6.6 summarizes the experimental S11 measurement as a func-

tion of modulation frequency for three different bias voltages. A reflection coefficient of

S11 <−8 dBe is obtained up to 40 GHz.

0 5 10 15 20 25 30 35 40-35

-30

-25

-20

-15

-10

-5

0

|VEAM

|

Laser off50WAC termination

Inputm

atc

hS

11

[dB

e]


0V

-3V

EAM voltage variedin steps of 1V

DUT

ILD

RL

50

S11

Signalsource

Fig. 6.6: Electrical reflection coefficient S11 (input match) as a function of modulation frequencywith the traveling wave electrode terminated with a load resistance RL = 50 Ω.

6.3. Dynamic intensity modulation response 81

Electrical transmission coefficient S21

The electrical transmission characteristics were performed as a preliminary characterization

of the electrode and simultaneous assessment of the modulation bandwidth.

0 10 20 30 40 50 60-6

-5

-4

-3

-2

-1

0Laser off50WAC termination

-3V

0V

EAM voltage variedin steps of 1V

|VEAM

|

Ele

c.transm

issi

on

S21[d

Be]


DUT

ILD

RL

50

Signalsource

S21

Fig. 6.7: Electrical transmission coefficient S21 for several EAM reverse bias voltages with thetraveling wave electrode terminated with a load resistance RL = 50 Ω.

A 3 dBe cutoff frequency of nearly 40 GHz can be observed as predicted using the simple

lumped element model. With increasing EAM reverse bias, the depletion width widens

thereby decreasing the capacitance of the p-i-n structure. Thus for high EAM reverse bias,

the EAM capacitance decreases eventually leading to enhanced modulation bandwidth. The

small undulations observed in the transmission measurements are a combination of small

internal reflections occurring in the electrical circuitry and the injecting probes.

6.3 Dynamic intensity modulation response

6.3.1 Small-signal response

The electro-optic response (E/O) is a convenient way of studying the modulation charac-

teristics of the EML under small-signal modulation conditions. A small sinusoidal signal

(≤ 200 mVpp) is applied to the EAM by biasing the EAM at the voltage of interest.

Fig. 6.8 (a) shows the experimental small-signal electro-optic response SEO of the 1310 nm

EML for several EAM reverse bias voltages. During the measurement, the laser was biased

at 85 mA with the traveling wave electrodes terminated with a 50 Ω resistor to improve RF

matching. Fig. 6.8 (b) shows the small-signal modulation bandwidth (3 dBe cutoff frequency)

as a function of EAM bias. The laser current was held constant during the measurements.


0 10 20 30 40 50-12

-9

-6

-3

0

3

-1.5V

ILD = 85mAT=15°CLEAM = 130µm = 1309nm R

el. E

/O re

spon

se [d

Be]


-1V

-1.25V

-1.75V

50 AC termination

(a) E/O response

-2.0 -1.5 -1.0 -0.5 0.0 + 0.5 + 1.00

5

10

15

20

25

30

3550 AC termination

ILD = 85mAT=15°CLEAM = 130µm = 1309nm

3dBe

cut

off f

requ

ency

[GH

z]

EAM bias [V]

(b) Small-signal bandwidth

Fig. 6.8: (a) Experimental electro-optic small-signal response SEO of the 1310 nm EML for fourdifferent EAM bias values in steps of 0.25 V, with the laser biased at 85 mA (b) small-signal mo-dulation bandwidth as a function of EAM bias. An optimum modulation bandwidth is obtainedbetween −1 V and −1.5 V EAM bias.

It is apparent from the plot that the modulation bandwidth increases steeply from about

5 GHz at 0 V to about 32 GHz at −1.5 V EAM bias. The dependence of the modulation

bandwidth with EAM bias can be predominantly attributed to the depletion width dpin de-

pendence of the p-i-n structure which ultimately determines the EAM capacitance. This

explains the steep increase in the small-signal modulation bandwidth from about 5 GHz at

0 V to about 18 GHz at −0.25 V (i.e., by a factor of about 3.6). Put in other words, the

small-signal modulation around 0 V includes the diffusion capacitance of the device which

comes into play during the positive half cycle of the sinusoidal modulation, whereas that of

the −0.25 V lies entirely in the reverse biased region of the EAM (for modulation amplitudes

noted previously).

The reduction in bandwidth is much more pronounced when the EAM is modulated under

completely forward biased conditions (below the turn-on voltage). The modulation band-

width increases relatively slowly above −1 V and reaches a maximum value of about 32 GHz

near −1.5 V. Increasing the reverse bias any further severely restricts the detected power

which increases the measurement uncertainty. Hence, there exists an optimum EAM bias

for which the modulation bandwidth and optical power is optimal. Thus, these small-signal

results form a starting point for the large-signal modulation analysis and time-resolved chirp

measurements.


6.3.2 Large-signal modulation results

Large-signal modulation experiments were performed to study the high-speed performance

by terminating the traveling wave electrode by a 50 Ω matching resistor. Fig. 6.9 shows the

screenshot of the large-signal modulation characteristics. A PRBS sequence of length 27 − 1

with a peak-to-peak modulation swing of Vpp = 2 V was used for driving the EAM, the

EAM biased at −1.1 V. The laser current and temperature settings remain identical to the

small-signal modulation presented in the previous section.

Fig. 6.9: A screenshot of 40 Gbps large-signal modulation response of the 1310 nm EML for anEAM bias of −1.1 V (typographical error in screenshot reading −1 V) at a laser current of 85 mAat 15 C. The results have been replotted in Fig. 6.10 for clarity.

For clarity, the electrical and optical waveforms in Fig. 6.9 have been replotted in Fig. 6.10

using the same timescale as that of the screenshot. Additionally, the optical waveform is

presented in optical power units (W) using the responsivity value of the photodiode employed

for detection.

Fig. 6.10 (a) shows the electrical modulating signal with a voltage swing of 2 Vpp and Fig.

6.10 (b) its corresponding optical response. The presented waveforms are averages of 1024

waveforms. The measured dynamic extinction ratio is about 8.3 dB. One could clearly observe

that the optical response follows the electrical signal, which demonstrates the high-speed

performance of the device.


0 100 200 300 400 500 600 700 800 900 1000

0

250

500

750

-2

-1

0 Electrical

ILD = 85mAVEAM = -1.1VVpp = 2VT = 15°C

Pow

er in

fibe

r [µW

]

Time [ps]

(b)

(a)

Optical

Elec

. sig

nal [

V]

Fig. 6.10: (a) PRBS electrical signal of word length 27 − 1 with a peak to peak voltage swingof 2 Vpp (b) corresponding experimental 40 Gbps large-signal modulation response of the 1310 nmEML for an EAM bias of −1.1 V, laser biased at 85 mA at 15 C.

6.4 Dynamic frequency modulation response

6.4.1 Small-signal chirp

In addition to the large-signal modulation characteristics, the chirping behavior of the device

is of considerable interest. The small-signal chirp of the EML was measured in accordance

with the description given in Sect. 4.2. A dispersion shifted fiber of length 22 km was used

for the investigations. The total dispersion of the link was obtained (also in accordance

with Sect. 4.2) from the slope of the straight line fit of the frequency nulls occurring in the

small-signal electro-optic response. The total dispersion of the link at the EML wavelength

corresponds to −396 ps/nm.

The EAM was biased at the voltage of interest and the obtained small-signal response was

propagated through the DSF dispersive link. The total response was then finally detected

at a network analyzer. The procedure was repeated for different voltage values. The E/O

6.4. Dynamic frequency modulation response 85

0 5 10 15 20 25 30 35 40

-110

-100

-90

-80

-70

-60

-2.5V

0V

ILD = 85mAT = 15°C=1309nm

50 AC terminationLDSF = 22km

|VEAM|

EAM reverse bias voltage varied in steps of 0.25V

E/O

resp

onse

[dBe

]


(a) E/O response after fiber

-2.5 -2.0 -1.5 -1.0 -0.5 0.0

-2.0

-1.5

-1.0

-0.5

0.0

+ 0.5

+ 1.0

ILD = 85mAT = 15°C=1309nmSm

all-s

igna

l H-p

aram

eter

EAM bias [V]

(b) Small-signal chirp-parameter

Fig. 6.11: (a) Experimental electro-optic small-signal response of the 1310 nm EML featuringdips after transmission through a dispersion-shifted fiber (DSF) of link length 22 km. The totaldispersion of the link is −396 ps/nm at the EML emission wavelength (b) extracted αH-parametervalues. Increasing the EAM reverse bias enables negative chirp-parameter values.

small-signal response features sharp dips due to the simultaneous interference between the

carrier and the sidebands. Using the total dispersion and length of the fiber link employed,

the small-signal chirp-parameter values were calculated by performing a fit to the dip fre-

quencies. The extracted values are plotted in Fig. 6.11 (b). The αH−parameter assumes

positive values for an EAM bias voltage of 0 V and monotonically decreases with increasing

reverse bias. Close to −0.95 V bias it assumes values of zero. Under deep reverse biasing

conditions, say at −1.5 V, it even assumes negative values. The comb of dip frequencies shift

toward smaller modulation frequencies with increasing negative chirp-parameter owing to

the negative dispersion coefficient of the fiber at the EML wavelength.

Although deep reverse biasing enables negative chirp-parameters, the EML suffers very high

insertion losses for bias values below −1.25 V, as can be observed from Fig. 6.1. The un-

certainty in the chirp-parameter extraction increases for increasing reverse bias values due

to high insertion loss incurred as is evident from the −2.5 V experimental curve. Almost

all commercial amplifiers available in the 1310 nm wavelength window, for boosting power

levels are semiconductor optical amplifiers. Since a semiconductor optical amplifier imposes

additional chirp to the incoming signal [50], the use of such amplifiers inevitably end up in

unreliable results. Hence, all the chirp investigations of 1310 nm EMLs carried out in this

work were performed without external optical amplification. This applies to the time-resolved

chirp measurements presented in the later part of the chapter as well.


Comparison with theory

The calculated chirp-parameter values using the Kramers-Kronig relations are presented in

Fig. 6.12 for several wavelength detuning values (read from the calculations presented in

Sect. 4.1). For easy interpretation, the operating wavelengths – corresponding to room tem-

perature wavelength detuning – are included as a legend.

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5

-2.0

-1.5

-1.0

-0.5

0.0

+ 0.5

+ 1.0

+ 1.5

+ 2.0

1300nm 1305nm 1310nm 1315nm 1320nm 1325nm

Wavelength detuning

40nm35nm30nm25nm

15nm

20nm

H-p

aram

eter

EAM bias [V]

Fig. 6.12: Calculated chirp-parameter values extracted from Kramers-Kronig transformation re-sults presented in Sect. 4.1. The calculations pertain to a measurement temperature of 25C. Thelegends correspond to the wavelength of operation at 25C.

There is a subtle difference between the experimental small-signal and the Kramers-Kronig

transformed chirp-parameter values. The Kramers-Kronig relations use the absorption change

at a specific EAM bias with respect to a reference EAM bias, in our case, the 0 V absorp-

tion curve. Therefore, the calculated αH values are linear approximations between the EAM

bias under consideration and 0 V. This also explains the missing chirp-parameter at 0 V in

Fig. 6.12, due to the absence of a reference absorption curve. By contrast, the small-signal

αH values are determined at specific bias voltages by probing the extinction curve. Thus,

the values obtained depend on local changes in the complex modal refractive index with

hardly any dependence on the amplitude of the small-signal used for investigation. Thus un-

der small-signal conditions (m ≪ 1), one virtually measures the differential of the complex

refractive index.

In order to compare the experimental and calculated ones, the experimental small-signal

chirp-parameter presented in Fig. 6.11 is fitted using a linear relation. It can be adequately

described using the following relation:

αH = 1.03 +

(1.12

V

)

V − 2.5 ≤ V ≤ 0 (6.4)


The imaginary part of the modal differential index 〈dn′′〉 is obtained from the static extinction

curve in conjunction with Eq. (3.32). Using αH values and 〈dn′′〉, the real part of the modal

differential index 〈dn′〉 is calculated.

-2.0 -1.5 -1.0 -0.5 0.0

-1.5

-1.0

-0.5

0.0

+ 0.5

+ 1.0

+ 1.5 differential modalimaginary index (<dn">)

differential modalreal index (<dn'>)

Diff

eren

tial m

odal

co

mpl

ex re

fract

ive

inde

x [x

10-4

]

EAM bias [V]

Fig. 6.13: Differential modal complex refractive index as a function of EAM bias.

Integrating the differential entities in Fig. 6.13 between the voltage points of interest, for

instance, between 0 V and −1 V yields the aggregate change in the complex index. αH-values

of +0.35 and −0.19 are obtained at −1 V and −2 V, respectively.

The emission wavelength of the EML is 1309 nm, i.e., it corresponds to a wavelength de-

tuning of 24 nm at 25C. Taking the small-signal αH-measurement temperature of 15C into

account (detuning increases by 4 nm), the revisited detuning is about 29 nm. Due to spatial

inhomogeneities of the PL wavelength across the wafer, the net detuning amounts to 23 nm.

The extracted values are in excellent agreement with the values reported for 20 nm detuning

in Fig. 6.12. The qualitative trend of decrease of chirp-parameter with increasing reverse bias

is also clearly observed. Thus, both the Kramers-Kronig transformations and small-signal

chirp-parameter estimation methods yield similar results within the range of interest of the

EAM bias voltage. In spite of this justification one should note that, the obtained mea-

surement results in both the methods are highly dependent on the local PL wavelength and

hence a direct comparison between them can be made only if the absorption characteristics

of the devices concerned are nearly identical.

6.4.2 Time-resolved chirp

Dynamic chirp analysis was done by tuning the experimental setup and locking the carrier

frequency λDFB at the discrimination points of the interferometer transmission curve and cap-

turing the waveforms at an oscilloscope. During the measurements, the chip was temperature


controlled to better than ±0.05C to guarantee wavelength stability. Fig. 6.14 shows the ex-

tracted intensity modulation (IM) component and the accompanying carrier frequency chirp,

after calibrating the Fabry-Perot resonator dispersion effects. The large-signal instantaneous

frequency excursion is directly proportional to the time varying chirp-parameter (voltage

dependent) and the time derivative of the relative power changes, as given by Eq. (3.43). A

peak to peak frequency deviation of around 7 GHz can be observed. The instantaneous fre-

quency increases during the rising edge and decreases during the trailing edge of the optical

pulse. Such a frequency change is encountered for an effective positive αH value.

0 200 400 600 800 1000-8

-6

-4

-2

0

2

4

6

8

0

50

100

150

200ILD = 85mAVEAM = -1VVpp = 2VT = 15°C

Chi

rp [G

Hz]

Time [ps]

Ext

ract

ed IM

[µW

]

Fig. 6.14: Experimental 40 Gbps time-resolved chirp of the 1310 nm EML for a laser current of85 mA and an EAM bias of −1 V at 15 C. A PRBS electrical signal of word length 27−1 with a peakto peak voltage swing of 2 Vpp was used for the measurements. Shown are the extracted intensitymodulation component and the accompanying frequency chirp, after calibrating the Fabry-Perotresonator dispersion effects.

An effective chirp-parameter αH−eff of + 0.43 was extracted by using the method of least

squares, which essentially starts with an arbitrary chirp-parameter and iteratively forces the

calculated results to agree with the measured ones. The extracted IM, which comprises

optical losses and the 3 dB transmission losses, is an indirect way of measuring the large-

signal modulation characteristics. However the extracted IM plot is included here, to validate

the suitability of the TRC setup up to 40 Gbps.

Chapter 7

1550 nm Electroabsorption ModulatedLasers

Motivated by the worlds growing need for communication bandwidth, progress is constantly

being reported in building novel optical fibers that are capable of handling the rapid increase

in data traffic. However, building an optical fiber link is a major investment, one that is very

expensive to replace. The optical fiber cables that were installed during the early 80’s consist

of millions of kilometers of standard single-mode fiber (SSMF) around the globe. Since old

optical fibers cannot be easily replaced with newer ones, innovative methods of exploiting the

available bandwidth are crucial. Even today, standard single-mode fibers are substantially

cheaper than the dispersion shifted fibers (DSF). Availability of erbium-doped fiber amplifiers

provides further motivation for transmission in the 1550 nm wavelength window. However,

the major impairment that restricts the performance of the 1550 nm wavelength window is

the chromatic dispersion. SSM fibers show a dispersion coefficient of +17 ps/(nm·km) which

result in enhanced pulse distortion due to the finite spectral width of a pulse. The constraint

to increase distance-bandwidth product of such SSM fibers without being obliged to under-

take significant infrastructural changes forms the motivation behind the development of low

or negatively chirped transmitters.


in this work, feature a multiple quantum well active layer with dual quantum well type:

3×5 nm thick and 8×7.5 nm thick quantum wells. The photoluminescence (PL) wavelengths

of 8 × 7.5 nm thick quantum wells and 3 × 5 nm thick quantum wells at room temperature

and under low excitation conditions are 1510 nm and 1540 nm, respectively. The wavelength

detuning, in this case, is defined from the shortest of the two PL wavelengths; i.e., from

1510 nm. The thickness of the intrinsic area (total thickness contribution from QWs, barriers,

spacers and separate confinement heterostructures) is 272 nm. The operating wavelength of

the device is near 1563 nm.

89



Fig. 7.1 shows the experimental light-current characteristics of a 1550 nm EML in continuous

wave (CW) operation for various EAM reverse bias voltages. The DFB laser and EAM

sections of the investigated EML are 370µm and 115µm long, respectively.

0 20 40 60 80 1000

100

200

300

400

500

600

700

800

-3V

-2V

-1V

|VEAM|

Pow

er in

fibe

r [µW

]

Laser current [mA]

T = 40°Ccw operation

0V


(a) L − I characteristics

0 20 40 60 80 1000

2

4

6

8

10T = 40°Ccw operation

0V

-1V

-2V

|VEAM|

EA

M p

hoto

curr

ent [

mA

]

Laser current [mA]

-3V


(b) EAM photocurrent

Fig. 7.1: (a) Experimental light-current characteristics of a 1550 nm EML in continuous waveoperation for various EAM reverse bias voltages. A heat-sink temperature of 40 C was chosen toprovide sufficient gain and absorption change in the laser and modulator sections, respectively (b)detected modulator photocurrent increases with increasing EAM reverse bias voltage. DFB laserand EAM sections are 370µm and 115µm long, respectively.

A measurement temperature of 40C was chosen to decrease the wavelength detuning by

≈ 6 nm (with respect to room temperature operation; 25C). This ensures sufficient gain and

optimum absorption swing in the laser and modulator sections, respectively. Fiber-coupled

optical power values at 0 V EAM bias lie in the range of 700µW. Light extinction can be

observed for increasing EAM reverse bias.

The thermal roll-over of the L − I curves becomes pronounced at high laser currents and

as well as at large reverse bias values due to self heating of EAM and laser sections [49, 67].

A relatively high laser threshold of 38 mA is due to the larger DFB wavelength detuning

from the absorption edge of the modulator. A larger detuning facilitates a high reverse bias

operation of the EAM which eventually increases the effective field available for drawing the

carriers from the active region. Moreover with increasing field, the tunneling barrier poten-

tial decreases exponentially [68,69] thereby reducing hole pile-up effects. However, too large

bias values inevitably deteriorate exciton stability [69] and the available optical power.

7.1. Static characteristics 91

-5 -4 -3 -2 -1 00

5

10

15

20

25

30

Extin

ctio

n [d

B]

EAM bias [V]

ILD = 80mAT = 40°C

= 1563nm

(a) Static extinction

1555 1560 1565 1570-90

-80

-70

-60

-50

-40

-30

-20ILD = 80mAVEAM = 0VT = 40°C

Pow

er [d

Bm]

Wavelength [nm]

(b) Spectral behavior

Fig. 7.2: (a) Experimental static light extinction characteristics of the 1550 nm EML at a heat-sinktemperature of 40C, the laser biased at 80 mA. Light extinction of up to 29 dB can be observedfor a voltage swing of 5 V (b) measured optical spectrum showing a lasing wavelength of around1563 nm at a temperature of 40C, the laser biased at 80 mA and the EAM at 0 V.

Fig. 7.2 (a) shows the static light extinction characteristics of the EML at a heat-sink tem-

perature of 40 C, the laser biased at 80 mA. Light extinction of up to 29 dB was measured

for a voltage swing of 5 V. A maximum extinction slope of 13.5 dB/V is achieved at a reverse

bias of −3 V. The spectral characteristics are shown in Fig. 7.2 (b). The lasing wavelength is

centered near 1563 nm at the measurement temperature 40 C, the laser biased at 80 mA and

the EAM at 0 V. Unfortunately, the EML does not operate under single longitudinal mode.

A side mode suppression of only 14 dB is obtained.

Temperature dependence

The temperature dependence of light-current (L − I) characteristics in continuous wave op-

eration is presented in Fig. 7.3. The measurements were performed between 20C and 75C

in steps of 5C.

The L − I curve corresponding to 20C shows a sharp kink around 70 mA of laser current.

This is attributed to the fact that, due to the inherent larger wavelength detuning of the

1550 nm EMLs, the gain at the operating wavelength (λDFB ≈ 1563 nm) is too low and con-

sequently Fabry-Perot modes dominate until 70 mA. The Fabry-Perot modes predominantly

occur in the short wavelength side of the spectrum due to the larger gain available here, with

the peak gain occurring near 1520 nm. Since high gain values occur close to the absorption

edge of the modulator most of the power (contributed by the Fabry-Perot modes) gets ab-

sorbed in the EAM section. Increasing the laser current further suppresses the multi-mode

operation consequently favoring the DFB mode. The DFB mode, being on the long wave-


0 20 40 60 80 1000

200

400

600

800

1000 30°C40°C

50°C

60°C

70°C

25°C

20°C

Temperature

Temperature varied in steps of 5°C

cw operationVEAM = 0V

Pow

er in

fibe

r [µW

]

Laser current [mA]

Fig. 7.3: Experimental light-current characteristics of the 1550 nm EML in continuous wave oper-ation for several different temperatures.

length side experiences less absorption which corresponds to the linear part of the rest of

the curve. Extrapolating the linear portion yields a threshold current of about 48 mA at 20C.

Increasing the heat-sink temperature, e.g. to 40C, increases the gain at the operating wave-

length due to the shift of the gain spectrum toward longer wavelengths by about +0.5 nm/K

(nanometer per Kelvin) in the 1550 nm wavelength window. This red-shift is simultaneously

accompanied by a slight broadening of the gain spectrum as schematically illustrated in

Fig. 7.4.

DFB

Wavelength

Modal

gai

n

T=40°C

T=20°C

+0.5 nm/K+0.1 nm/K

Fig. 7.4: Schematic representation of temperature dependence of modal gain at the wavelength ofoperation λDFB. The peak wavelength of the gain spectrum shifts toward longer wavelengths by+0.5 nm/K and λDFB by +0.1 nm/K in the 1550 nm wavelength window. The relative shift of thepeak wavelength of the gain spectrum with respect to λDFB is thus +0.4 nm/K.


In addition, λDFB red-shifts by +0.1 nm/K in the 1550 nm wavelength window. Thus, the

relative shift of the peak wavelength of the gain spectrum with respect to λDFB is +0.4 nm/K.

This red-shift of the gain peak wavelength is a result of bandgap shrinkage [3,6,27] occurring

at elevated temperatures. Due to the larger gain at 40C the threshold current apparently

decreases to 38 mA. The most notable feature is that the threshold current shows only a slight

increase from 38 mA at 40C to 42 mA at 75C. The threshold current, hardly showing any

dependency between 40C and 75C indicates that the gain spectrum is relatively flat and

thus the shift of the gain peak wavelength has no profound influence on the laser threshold

(within the temperature regime under consideration). The relatively flat gain spectrum is a

consequence of the exploitation of dual quantum well types with two different photolumines-

cence (PL) wavelengths for the active layer. This is because, the total gain spectrum is the

sum of gain contributions of 8× 7.5 nm (gain contribution near 1520 nm) and 3× 5 nm (gain

contribution near 1550 nm) thick quantum wells.

For a heat-sink temperature of 70C, the maximum optical power coupled into the single-

mode fiber is about 280µW. The reduction in power at higher temperatures is primarily due

to the relative shift of the absorption spectrum of the EAM by +0.4 nm/K [32,34]. Thus, the

increased residual absorption at higher temperatures restricts the obtainable optical power

severely. Other mechanism which simultaneously reduces power at higher temperatures can

be attributed to the increased nonradiative recombination (Auger and defect recombinations)

occurring at elevated temperatures [27,37].



The small-signal electro-optic (E/O) response of the 1550 nm EML is shown in Fig. 7.5.

Measurement conditions pertain to a temperature of 40C with the laser biased at 80 mA and

0 10 20 30 40 50-12

-9

-6

-3

0

350 AC termination

ILD = 80mAT = 40°CLEAM= 115µm = 1563nm

-2.0V

-2.5V

Rel

ativ

e E/

O re

spon

se [d

Be]


Fig. 7.5: Experimental electro-optic small-signalresponse of the 1550 nm EML for two differentbias voltages of −2.0 V and −2.5V at a temper-ature of 40C. A 3 dBe cutoff frequency of about33 GHz can be observed.


the traveling wave electrode AC terminated by a 50 Ω resistance. A 3 dBe cutoff frequency

of about 33 GHz is obtained for EAM bias voltages between −2 V and −2.5 V. This range of

optimum EAM bias shall be used for the large-signal investigations.


As a rule of thumb, a small-signal modulation bandwidth of ≈ 0.7×BR is required for en-

coding non-return to zero (NRZ) signals at a bit rate of BR. The obtained small-signal

bandwidth of 33 GHz is greater than the modulation bandwidth required (≈ 28 GHz) for

40 Gbps NRZ applications.

0.8

5V

/div

10 ps/div

Fig. 7.6: Electrical PRBS signal of wordlength 211 − 1 with a peak to peak voltageswing of 2.5 Vpp used for large-signal modu-lation investigations at 40 Gbps.

Fig. 7.7: Optical eye diagram at 40 Gbpswith VEAM = −2.5V; ILD=80 mA; T = 40C.A dynamic extinction ratio of 10.5 dB andaverage fiber-coupled optical power of 1 mWis obtained with 6 dB external amplification.

In order to confirm this prediction experimentally, an electrical PRBS drive signal of word

length 211 − 1, shown in Fig. 7.6, is applied to the EAM. The peak to peak voltage swing is

2.5 Vpp. Fig. 7.7 shows the corresponding optical eye diagram at 40 Gbps, biasing the EAM

at −2.5 V. A dynamic extinction ratio of 10.5 dB has been measured at a temperature of

40C. An average (i.e., mean modulated) fiber-coupled optical power of 1 mW is obtained

after external amplification using an erbium-doped fiber amplifier. The wide open and sym-

metric eye diagram demonstrates the high-speed modulation performance of the device as

predicted from the small-signal results.

The influence of various parameters on the large-signal behavior of the device is investigated

in the following. The parameters under consideration are the laser current, EAM bias and

temperature. In all the cases, the peak to peak voltage swing was held constant and an

external amplification of ≈ 6 dB was used. Finally, a summary of average optical power and

dynamic extinction ratio is presented.


(a) Laser current dependence

Fig. 7.8 (a) shows eye diagrams at 40 Gbps recorded to study the influence of laser current on

the large-signal modulation characteristics. Increasing the laser current results in increased

average output power up to 80 mA and is hardly affected thereafter. However, one can

observe that the distribution of the ‘1’ level in the eye diagram becomes broader owing

to speculated modal instabilities encountered for laser currents above 80 mA. Thus, in the

forthcoming investigations, the laser current will be held constant at 80 mA to study the

influence of other parameters.

(b) EAM bias dependence

The optimum operation point of the EML was studied by varying the EAM bias voltage

along the static extinction curve shown in Fig. 7.2 (a). Fig. 7.8 (b) shows the corresponding

eye diagram measurements performed at 40 Gbps with EAM bias as a variable.

For very low or very high reverse bias values, the modulation efficiency decreases due to

increasing nonlinearity of the extinction curve. For instance, at EAM bias values of −1.5 V

or −3.5 V the eye pattern degrades with the eye cross-over point lying well below 50%. On

the other hand at −2.5 V, EAM bias wide open and symmetric eye diagrams are obtained

with the eye cross-over occurring near 50%. Thus, the optimum bias at the temperature of

operation (40C) is around −2.5 V.

(c) Temperature dependence

Owing to the characteristic steep absorption slope close to the band edge, QCSE based

EAMs are inherently sensitive to temperature [6]. With increasing temperature, the transi-

tion energy between the electron ground state and heavy hole (HH) ground state decreases.

This reduction in the transition energy with temperature can be adequately explained by

the empirical Varshni relations [40,70].

The corresponding experimental shift of the EAM absorption spectrum with temperature, in

the 1550 nm wavelength window, is ≈ 0.5–0.6 nm/K. Simultaneously, with rise in tempera-

ture, the modal effective refractive index 〈n′

eff〉 in the laser section increases by ≈ 2.1×10−4/K.

This results in a red shift of the operation wavelength, λDFB, by ≈ 0.1 nm/K.

The net effect is a decrease of the detuning between the absorption edge of the EAM and the

laser emission wavelength by ≈ 0.4–0.5 nm/K. This considerably degrades the EML dynamic

performance in the absence of any temperature control as illustrated in Fig. 7.8 (c).

-1.5V -2.0V -2.5V -3.0V -3.5V

475µ

W/d

iv

10 ps/div

60mA 70mA 80mA 90mA

475 µ

W/d

iv

10 ps/div

100mA

20°C 30°C 40°C 50°C 60°C

475µ

W/d

iv

10 ps/div

(b)

(a)

(c)

T = 40°C; V = -2.5VEAM

I =LD

T = 40°C; I = 80mALD

I = 80mA;V = -2.5VLD EAM

V =EAM

T =

Fig. 7.8: Experimental 40 Gbps eye diagrams of the 1550 nm EML. Shown are the (a) laser current (ILD) dependence (b) EAM bias(VEAM) dependence (c) temperature (T ) dependence, with the EAM driven by a peak to peak modulation voltage of Vpp = 2.5V.


The increase in residual absorption at the operating wavelength contributes predominantly

to the reduction of average optical output power. Other parameters which simultaneously

influence the optical power can be attributed to the temperature dependent nonradiative

recombination mechanisms and the slight dependency of the laser threshold current (Fig. 7.3)

that reduce the optical power delivered by the DFB laser.

50 60 70 80 90 1000.00.20.40.60.81.01.21.4

0

2

4

6

8

10

12

T = 40°CVEAM= -2.5VVpp = 2.5V

Aver

age

pow

er [m

W]

Laser current [mA]

Dyn

amic

ext

inct

ion

[dB]

(a) Laser current dependence

-4.0 -3.5 -3.0 -2.5 -2.0 -1.50.00.20.40.60.81.01.21.4

0

2

4

6

8

10

12

Aver

age

pow

er [m

W]

EAM bias [V]

T = 40°CILD = 80mAVpp = 2.5V

Dyn

amic

ext

inct

ion

[dB]

(b) EAM bias dependence

10 20 30 40 50 60 700.00.20.40.60.81.01.21.4

0

2

4

6

8

10

12

Aver

age

pow

er [m

W]

Temperature [°C]

ILD = 80mAVEAM= -2.5VVpp = 2.5V

Dyn

amic

ext

inct

ion

[dB]

(c) Temperature dependence

Fig. 7.9: Summary of average optical power and dynamic extinction ratio of 40 Gbps large-signalmodulation results of the 1550 nm EML (a) laser current dependence (b) EAM bias dependence (c)temperature dependence.

The average fiber-coupled optical power and the dynamic extinction dependence on the

different parameters studied are summarized in Fig. 7.9. The laser current shows a weak de-

pendency as shown in Fig. 7.9 (a). However, the EAM bias and the temperature significantly

influence the large-signal modulation performance.

For instance, in Fig. 7.9 (b) the optical power steadily decreases with increasing EAM reverse


bias as expected from the characteristic light extinction behavior of an EAM. Optimum dy-

namic extinction values of about 10 dB are restricted to a narrow EAM bias range of −2.5 V

to −3 V corresponding to the bias regime where modulation efficiency is a maximum.

Temperature dependent average power and dynamic extinction are summarized in Fig. 7.9 (c).

The average optical power in fiber drops from 1.3 mW at 20C to about 0.36 mW at 60C.

This drop in optical power is predominantly attributed to the increase in the ‘ON’ state

insertion loss at the operating wavelength. On the contrary, the dynamic extinction ratio

increases from about 6 dB at 20C to nearly 12 dB at 50C. This is simply the result of in-

creasing absorption swing with decreasing wavelength detuning, which is however obtained

at the expense of optical power. The chosen EAM bias voltage delivers an optimum per-

formance at 40C with more than 10 dB dynamic extinction and a mean modulated optical

power of 1.0 mW in fiber. For temperatures above 50C, no reliable estimate of the dynamic

extinction was possible due to low available power.

7.3 Semi-cooled electroabsorption modulated lasers

The effect of temperature on the large-signal modulation characteristics was illustrated in

Fig. 7.8 (c) and Fig. 7.9 (c). The average optical power and the dynamic extinction ratio

were found to degrade considerably when the temperature was varied from 20C to 70C. In

order to employ EMLs over a wide temperature change without active temperature control,

the average power and the dynamic extinction ratio values must stay nearly constant. Such

temperature independent performance of electroabsorption modulated lasers over a limited

temperature range is termed as semi-cooled operation. Such semi-cooled operation, for in-

stance, is highly desirable for cost-effective solutions. For example, the 10 Gigabit small form

factor pluggable (XFP1) transceivers are gaining popularity due to their small form factor

and low power consumption, typically less than 3.5 W.

To investigate the possibility of such semi-cooled operation, temperature dependent static

extinction measurements were performed and the experimental results are presented in the

following.

Fig. 7.10 shows the static light extinction characteristics of the EML as a function of tem-

perature, the laser biased at 80 mA. The following characteristic feature can be observed.

The maximum extinction slope shifts toward low reverse bias voltages with increasing tem-

perature. For instance, the maximum extinction slope occurs near −2.85 V at 20C while

for the case of 65C it occurs near −1.55 V. Moreover, it is apparent from Fig. 7.10 that the

absolute power falls considerably with temperature for the optimum EAM bias chosen for

1Supports OC192/STM-64, 10 G Fibre Channel, G.709 and 10 G Ethernet, usually with the same mod-ule [71].

7.3. Semi-cooled electroabsorption modulated lasers 99

room temperature operation. This is also evident from the dynamic measurements presented

in Fig. 7.8 (b).

-5 -4 -3 -2 -1 0 10

100

200

300

400

500

600

700


ILD = 80 mALEAM = 115µm = 1563 nm

Temperature

25°C35°C

45°C

55°C

65°C

Pow

er in

fibe

r [µW

]

EAM bias [V]

(a) Fiber-coupled power

-5 -4 -3 -2 -1 0 10

5

10

15

20

25

30

35


ILD = 80 mALEAM = 115µm = 1563 nm

Temperature25°C

65°C

Extin

ctio

n [d

B]EAM bias [V]

(b) Light extinction (logarithmic)

Fig. 7.10: Experimental (a) fiber-coupled power (b) logarithmic static light extinction character-istics of the 1550 nm EML as a function of temperature. The measurements pertain to a laser biasof 80 mA.

-5 -4 -3 -2 -1 0

0.0

0.2

0.4

0.6

0.8

1.0


ILD = 80 mALEAM = 115µm = 1563 nm

Temperature

20°C65°C

Nor

mal

ized

pow

er

EAM bias [V]

(a) Normalized power

10 20 30 40 50 60 70 80

-3.0

-2.5

-2.0

-1.5

-1.0VEAM [V] = -3.5 V+ (0.03)T*(V/°C)

Opt

imum

EAM

bia

s [V

]

Temperature [°C]

(b) EAM active bias control

Fig. 7.11: (a) Normalized power for different temperatures (b) active bias control for EAM andcorresponding empirical fit.

Fig. 7.11 (a) shows the normalized extinction curves in which the shift of the optimum bias

point with temperature is evident. The shift of the optimum bias point with temperature is

empirically fit to yield the following relation:


VEAM [V] ≈ −3.5 V + (0.03)T

[VC

]

20C ≤ T ≤ 70C (7.1)

From Eq. (7.1), it is evident that the optimum EAM bias voltage increases by 0.3 V per

10C rise in temperature. By actively controlling the EAM bias voltage in accordance with

temperature, one can expect that average optical power and dynamic extinction remain con-

stant. A plot of the empirical fit is shown in Fig. 7.11 (b). The solid circles in Fig. 7.11 (b)

correspond to the optimum EAM bias voltages used for subsequent large-signal modulation

measurements presented in Fig. 7.12. The empirical relationship given by Eq. (7.1) is ap-

plicable between 20C and 70C.

20°C 40°C

-2.85V

30°C

-2.60V -2.30V

475µ

W/d

iv

10 ps/div

VEAM

T

VEAM

T 70°C50°C 60°C

-1.40V-1.85V -1.60V

475µ

W/d

iv

10 ps/div

Fig. 7.12: Experimental 40 Gbps eye diagrams of the 1550 nm EML with active EAM bias control.The active bias control guarantees optimum EAM bias voltage for operating temperatures between20C and 70C. The peak to peak modulation voltage was Vpp = 2.5 V with the laser biased at80 mA.

The average optical power and the corresponding dynamic extinction ratios have been sum-

marized in Fig 7.13. It is quite evident that the average power and the dynamic extinction

remain almost constant from 20C to 70C. Dynamic extinction ratios of at least 8 dB and

an average optical power of at least 0.85 mW can be observed. An external amplification of

≈ 7 dB was used for the investigations.

The experimental results demonstrate the excellent dynamic performance of the electroab-

sorption modulated laser emitting in the 1550 nm wavelength window for operation between


20 30 40 50 60 700.00.20.40.60.81.01.21.4

0

2

4

6

8

10

12

Aver

age

pow

er [m

W]

Temperature [°C]

ILD = 80mAVEAM = active controlVpp = 2.5V

Dyn

amic

ext

inct

ion

[dB]

Fig. 7.13: Summary of average optical power and dynamic extinction ratio of 40 Gbps large-signalmodulation results of the 1550 nm EML with active bias control. The active bias control guaranteesoptimum EAM bias voltage for operating temperatures between 20C and 70C.

20C and 70C. Such semi-cooled operation reduces the on-chip power consumption required

for temperature control by about 2.2 W.


Small-signal chirp

Due to inherent large wavelength detuning of about 60 nm, the 1550 nm EMLs can be

expected to manifest a positive chirp-parameter for the range of EAM bias exploited for

modulation. A SSM fiber link of 50.5 km was used for the extraction of the small-signal

chirp-parameters. While performing measurements, an external amplification of ≈ 10dB was

provided by an erbium-doped fiber amplifier (EDFA2) to compensate the propagation loss

in the fiber. Fig. 7.14 summarizes the experimental results as a function of EAM bias. With

increasing reverse bias, the magnitude of the chirp-parameter decreases, but as predicted

from the Kramers-Kronig calculations in Fig. 4.3, it still assumes positive values even for

deep reverse biasing.

Fig. 7.14 (b) summarizes the influence of laser current on the small-signal chirp-parameter.

One can observe a weak dependency on the laser current. The weak dependency is attributed

to the self heating of the laser section which red-shifts the absorption edge of the EAM and

thereby leading to decrease of the chirp-parameter. The results shall be compared with

similar measurements performed for EMLs integrated with SOAs.

2The life-time of the carriers in an EDFA is of the order of few milliseconds (ms) [63]. Thus, the incorpo-ration of an EDFA for data rates of interest, i.e., above 10Gbps, does not affect the chirp properties of theinvestigated EML.


-4 -3 -2 -1 0+0.4

+0.6

+0.8

+1.0

+1.2

+1.4

+1.6ILD = 80mAT = 40°C

Smal

l-sig

nal

H-p

aram

eter

EAM bias [V]

(a) EAM bias dependence

40 60 80 100 120 140+0.4

+0.6

+0.8

+1.0

+1.2

+1.4

+1.6VEAM = -2VT = 40°C

Smal

l-sig

nal

H-p

aram

eter

Laser current [mA]

(b) Laser current dependence

Fig. 7.14: Experimental small-signal αH dependency of the 1550 nm EML on (a) EAM bias and(b) laser current. Increasing the EAM reverse bias enables low chirp-parameter values. However,the inherent large detuning (of the 1550 nm EML design) allows for positive chirp-parameter valuesonly. A weak dependency on the laser current is observed.

Comparison with theory

The calculated chirp-parameter values using the Kramers-Kronig relations are presented in

Fig. 7.15 for several wavelength detuning values (read from the calculations presented in

Fig. 4.3 of Sect. 4.1). For easy interpretation, the operating wavelengths – corresponding to

room temperature wavelength detuning – are included as a legend.

The experimental small-signal chirp-parameter presented in Fig. 7.14 can be adequately

described using the relation:

αH = 1.50 +

(0.37

V

)

V +

(0.03

V2

)

V 2 − 4 ≤ V ≤ 0 (7.2)

Similar to the description presented in the previous chapter, the imaginary part of the modal

differential index 〈dn′′〉 is obtained from the static extinction curve in conjunction with

Eq. (3.32). Subsequently, using αH values and 〈dn′′〉, the real part of the modal differential

index 〈dn′〉 is calculated.

Integrating the differential entities presented in Fig. 7.16, yields the chirp-parameter between

the voltage points of interest. Chirp-parameter values of +1.3, +0.95, +0.83 are obtained at

−1 V, −2 V and −3 V bias, respectively.


-4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5-2.0

-1.5

-1.0

-0.5

0.0

+ 0.5

+ 1.0

+ 1.5

+ 2.0

30nm

40nm50nm

1535nm 1540nm 1545nm 1550nm 1555nm 1560nm

35nm

45nmWavelengthdetuning

25nmH-p

aram

eter

EAM bias [V]

Fig. 7.15: Calculated chirp-parameter values extracted from Kramers-Kronig transformation re-sults presented in Sect. 4.1. The calculations pertain to a measurement temperature of 25C. Thelegends correspond to the wavelength of operation at 25C.

-4 -3 -2 -1 0-2

-1

0

+ 1

+ 2

+ 3

+ 4

+ 5differential modalimaginary index (<dn">)

differential modalreal index (<dn'>)

Diff

eren

tial m

odal

co

mpl

ex re

fract

ive

inde

x [x

10-4

]

EAM bias [V]

Fig. 7.16: Differential modal complex refractive index of the 1550 nm EML as a function of EAMbias voltage.

The emission wavelength of the EML is near 1563 nm, i.e., it corresponds to a wavelength

detuning of 53 nm at 25C. Taking the small-signal αH-measurement temperature of 40C

into account (detuning decreases by 6 nm), the revisited detuning is about 47 nm. The inte-

grated small-signal chirp-parameter values at −1 V agrees very well with the value reported

for 45 nm detuning in Fig. 7.15. Thereafter, the small-signal chirp-parameter changes rela-

tively slowly as compared to the Kramers-Kronig results.

Chapter 8

1550 nm Electroabsorption ModulatedLasers Integrated with SOAs

Semiconductor optical amplifiers (SOAs) integrated with electroabsorption modulated lasers

(EMLs), abbreviated as EML-SOAs, offer the potential of boosting the optical output power

and partly compensating the EML chirp. This chapter summarizes the experimental results

of EML-SOAs emitting in the 1550 nm wavelength window. The active layer structure is

identical to that of the 1550 nm EMLs.


-5 -4 -3 -2 -1 0 10

500

1000

1500

2000

2500

3000

ISOA

ILD = 50mAT = 40°CLEAM = 130µmLSOA = 500µm = 1561nm

80mA

60mA

40mA

100mA

Pow

er in

fibe

r [µW

]

EAM bias [V]

(a) Fiber-coupled power

-5 -4 -3 -2 -1 0 10

5

10

15

2040mA

100mA

SOA current varied in steps of 10mA

ILD = 50mAT = 40°CLEAM = 130µmLSOA = 500µm = 1561nm

ISOA

Stat

ic e

xtin

ctio

n [d

B]

EAM bias [V]

(b) Light extinction (logarithmic)

Fig. 8.1: Experimental static light extinction characteristics of a 1550 nm EML-SOA for severalSOA currents. The results pertain to a temperature of 40C with the laser biased at 50 mA. Withincreasing SOA current, the optical power coupled into the fiber increases.

The static light extinction characteristics of the EML integrated with an SOA are presented

in Fig. 8.1. The length of the laser, EAM and SOA sections are 370µm, 130µm and 500µm,

104


respectively. The measurements pertain to a temperature of 40C with the laser biased at

50 mA.

With increasing SOA current, the optical power coupled into the fiber increases, for a constant

EAM bias, owing to amplification in the SOA section. For large SOA currents, and for deep

EAM reverse biasing there is still residual optical power coupled into the fiber. For instance,

for an SOA current of ISOA = 100 mA at an EAM bias of VEAM = −5 V a residual power

of ≈ 200µW can be observed. This is primarily attributed to the spontaneous emission

contribution of the SOA, since much of the light is absorbed in the EAM section under deep

reverse biasing conditions. In Fig. 8.1 (b), the corresponding extinction ratios are plotted

in the logarithmic scale. A maximum extinction ratio of nearly 17 dB is obtained for an

SOA pump current of 40 mA. The drop in extinction at large SOA currents is due to the

spontaneous emission contribution noted previously.



The small-signal electro-optic (E/O) response of the 1550 nm EML is shown in Fig. 8.2.

Measurement conditions pertain to a temperature of 40C with the laser biased at 50 mA.

As for the case of 1550 nm EMLs, a measurement temperature of 40C was chosen to decrease

the wavelength detuning.

0 10 20 30 40 50-12

-9

-6

-3

0

3

70mAVEAM = -2VILD = 50mAT = 40°CLEAM = 130µm = 1561nm

Rel

ativ

e E/O

resp

onse

[dBe

]


90mA

110mA

50 AC termination

Fig. 8.2: Experimental E/O response of the 1550 nm EML-SOA for three different SOA currentsat an EAM bias of −2 V at 40C. A 3 dBe cutoff frequency of around 32 GHz is obtained.

106 Chapter 8. 1550 nm Electroabsorption Modulated Lasers Integrated with SOAs

The experimental small-signal modulation bandwidth hardly shows any dependence on the

amplifier pump current. The modulation bandwidth is nearly 32 GHz, which is close to that

of the EML structures (without SOA) presented in the earlier chapter.


As noted in the previous chapter, the obtained small-signal modulation bandwidth f3dBe of

32 GHz is sufficient for 40 Gbps NRZ applications. Fig. 8.3 confirms this prediction experi-

mentally, whereby a peak to peak driver voltage swing of 2.5 V was applied by biasing the

EAM at −2 V.

0.8

5V

/div

10 ps/div

(a) Electrical eye (b) Optical eye

Fig. 8.3: (a) PRBS electrical drive signal of word length 211 − 1 (b) experimental 40 Gbps eyediagram of the 1550 nm EML-SOA for a peak to peak modulation voltage Vpp = 2.5 V, the EAMbiased at −2 V and the laser biased at 50 mA. A RF extinction ratio of 9.8 dB has been measuredat a temperature of 40C. An average fiber-coupled optical power of 1.15 mW is obtained.

A RF extinction ratio of 9.8 dB has been measured at a temperature of 40C with an av-

erage fiber-coupled optical power of 1.15 mW. The values illustrate the excellent dynamic

performance of the EML-SOA structure.

Amplifier current dependence

The effect of amplifier pump current on the large-signal modulation behavior is presented

in Fig. 8.4. Measurement temperature and driver voltage swing remain identical to the

conditions stated previously. One can observe that the average optical power increases with

increasing SOA pump current. For very strong amplifier currents, the ON state becomes

increasingly noisy due to possible back reflections occurring at the SOA facet.


80mA 90mA 100mA 110mAI =SOA

57

0 µ

W/d

iv

10 ps/div

Fig. 8.4: Experimental 40 Gbps large-signal modulation characteristics of the 1550 nm EML-SOAas a function of SOA current (ISOA) at 40C. The peak to peak modulation voltage was Vpp =2.5 V with the laser biased at 50 mA.

80 90 100 1100.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0

2

4

6

8

10

12

Aver

age

pow

er [m

W]

Integrated amplifier current [mA]

T = 40°CVEAM = -2VVpp = 2.5VILD = 50mA D

ynam

ic e

xtin

ctio

n [d

B]

Fig. 8.5: Summary of average optical power and dynamic extinction ratio of 40 Gbps large-signalmodulation results of the 1550 nm EML-SOA. Average fiber-coupled optical power levels in excessof 1 mW and a dynamic extinction of 9.8 dB are obtained at an amplifier current of 100 mA.

The average optical power and RF extinction values obtained at 40 Gbps are summarized

in Fig. 8.5. Average fiber-coupled optical power levels in excess of 1 mW and RF extinc-

tion between 8.6 dB and 9.8 dB is obtained. These measurement results demonstrate the

excellent high-speed performance of the EML-SOAs with adequate power and extinction

characteristics.

Bit error rate estimation at 10Gbps

Assuming Gaussian distribution for the two binary levels (‘1’ & ‘0’) an approximate value of

the bit error rate (BER) can be estimated. The BER so calculated is only a rough estimation

since it excludes fiber loss, dispersion and chirp related broadening effects. Fig. 8.6 shows

10 Gbps eye diagram measurements with corresponding histograms for the ‘1’ and ‘0’ levels.

The eye windows used for calculating the histograms correspond to 80% of the bit period.

108 Chapter 8. 1550 nm Electroabsorption Modulated Lasers Integrated with SOAs

(a) '1' level(a) '1' level (b) '0' level

570 µ

W/d

iv

20 ps/div

Fig. 8.6: Histogram measurements for bit error rate estimation of the 1550 nm EML-SOA at10 Gbps. Eye windows correspond to 80% of the bit period.

The quality factor Q and the bit error rate BER are estimated through the following relations:

Q =

(µ1 − µ0

σ1 + σ0

)

(8.1)

BER ≈ 1

2

[

1 − erf

(Q√2

)]

(8.2)

where µ1 and µ0 represent the mean, σ1 and σ0 the standard deviation values of the ‘1’ & ‘0’

levels, respectively. Plugging 20.3 mV and 2.46 mV for µ1 and µ0 respectively, and standard

deviations of 1.85 mV and 0.8 mV for σ1 and σ0 respectively, Q turns out to be 6.73. Using

the expression in Eq. (8.2) a bit error rate of ≈ 8.5 × 10−12 is estimated.


The dynamic electro-optic (E/O) small-signal response of the 1550 nm EML-SOA was ob-

tained by propagating the modulated signal along a link whose dispersion amounts to

+879 ps/nm at the EML emission wavelength. Fig. 8.7 (a) shows that for increasing laser

current, the comb of dip frequencies shift toward higher modulation frequencies. This is

because, with increasing laser current more and more of optical power is being pumped into

the SOA section.

For single-mode ridge waveguides, at power levels above −5 dBm, gain saturation in SOA in-

duces self phase modulation (SPM) [51], which lifts the symmetry of the modulated spectrum

with respect to the carrier frequency [28,54].


0 5 10 15 20 25 30-40

-30

-20

-10

0

10

13 16

50 AC term.LSSMF = 50.5km

ILD

Laser current variedin steps of 20mA

ISOA

= 100mAT = 40°C = 1561nm

Rel

. E/O

resp

onse

[dBe

]


140mA40mA

(a) E/O response after fiber

40 60 80 100 120 140-0.4

-0.3

-0.2

-0.1

0.0

+ 0.1

+ 0.2

+ 0.3

+ 0.4

+ 0.50.2 0.4 0.6 0.8 1.0 1.2 1.4

ISOA = 100mAVEAM = -2VSm

all-s

igna

l H-p

aram

eter

Laser current [mA]

T = 30°C T = 40°C

Approx. power coupled into SOA [mW]

(b) Small-signal chirp-parameter

Fig. 8.7: (a) Experimental electro-optic small-signal response of the 1550 nm EML-SOA featuringdips after transmission through a standard single-mode fiber (SSMF) of link length 50.5 km. Thetotal dispersion of the link is +879 ps/nm at the EML emission wavelength. (b) extracted αH-parameter values for two different temperatures. Increasing laser current drives SOA into saturationenabling very low or negative chirp-parameter values.

The optical power coupled into the SOA section was calculated assuming a modal residual

absorption of 60 cm−1, a modal absorption change of 260 cm−1 per 2 V with LEAM = 130µm.

A threshold current of 25 mA and 80% internal quantum efficiency (ηi) was assumed in the

laser section. For simplicity, the above values were assumed to be constant over the mea-

surement temperature range.

Extracted small-signal chirp-parameter values for two different temperatures are shown in

Fig. 8.7 (b). It is apparent that the small-signal chirp-parameter value decreases in magnitude

and assumes even negative values for strong laser pumping. The temperature dependency

of the chirp-parameter is superimposed on the same plot. Increasing the temperature from

30C to 40C decreases the chirp-parameter by about 0.2. This effect can be understood

if one considers the fact that increasing the temperature decreases the effective detuning

thereby yielding low or negative chirp-parameters.

Chapter 9

Conclusions

The ultimate aim of an optical communication system is to transmit the largest possible

data rate over the maximum possible distance guaranteeing a given system performance at

the lowest cost feasible. Besides optical nonlinearities, fiber loss and fiber dispersion are the

primary limiting factors of the transmission capability of single-mode systems, operating in

the 1310 nm and the 1550 nm wavelength windows, respectively.

Motivated by the above fact, the primary objective of this thesis was to investigate the fre-

quency chirping properties of electroabsorption modulated laser structures, since fiber dis-

persion interacts with device chirping thereby resulting in pulse distortion. The fabricated

devices were based on the InGaAlAs/InP material system employing an identical active area

for the distributed feedback (DFB) laser, electroabsorption modulator (EAM) and the (op-

tional) semiconductor optical amplifier (SOA) sections.

Three different methods have been invoked for studying the frequency chirping behavior.

In the first method, Kramers-Kronig transformations of the photocurrent absorption data

were used for extracting the modal refractive index changes and thus the chirp-parameter

values. The results were presented for electroabsorption modulated lasers emitting in the

1310 nm and the 1550 nm wavelength windows. The influence of device parameters, in par-

ticular the choice of operating wavelength λDFB, was shown to play a decisive role in de-

termining the sign and magnitude of the chirp-parameter. For this purpose, in Chapter 3,

experimental absorption spectra were used to illustrate the tight interplay between the ab-

solute power, static extinction and the frequency chirping behavior. For wavelength detuning

between 25–35 nm, the calculated chirp-parameter varied between +0.9 and +1.5 for a bias

voltage of −1 V and a peak to peak modulation voltage of 2Vpp. The corresponding max-

imum frequency chirp, calculated assuming a 40 Gbps pulse, remained practically constant

in the range of 7 GHz. It was also shown that although the maximum chirp dropped below

3 GHz for a wavelength detuning of 60 nm, the static extinction ratio dropped dramatically

to about 1–2 dB. Similarly, at very low wavelength detuning values of 15 nm, negative chirp-

parameters were obtained at −1 V bias, but the insertion loss increased dramatically to 35 dB.

110

111

Thus, the definition of the operation wavelength is restricted to a very narrow wavelength

window of about 20 nm for demanding high-speed applications. A wavelength detuning of

30 nm was found to deliver optimum performance in terms of frequency chirp, optical power

and static extinction ratio. At this detuning, the calculated maximum frequency chirp was

+7.5 GHz with an insertion loss of 8 dB and a static extinction ratio of 17 dB/2V.

The second method exploiting the frequency domain was based on the small-signal fiber

response method. This was employed to study the frequency chirping behavior by probing

the extinction curve at specific EAM bias voltages. For electroabsorption modulated lasers

emitting in the 1310 nm wavelength window a chirp-parameter of −0.5 was obtained at a

reverse bias voltage of −1.5 V. For the case of electroabsorption modulated lasers emitting in

the 1550 nm wavelength window, the chirp-parameter remained +0.9, i.e., positive, even for a

reverse bias voltage of −2 V. The relatively high value of the chirp-parameter is attributed to

the larger wavelength detuning employed in the 1550 nm EMLs. Thus, deep reverse biasing

was shown to achieve low or negative chirp-parameters.

The major part of the frequency chirp investigation was devoted to the time-resolved chirp-

ing behavior, i.e., the large-signal chirp or dynamic chirp. The principle of performing a

time-resolved chirp measurement exploiting the frequency dependent transmission proper-

ties of a Fabry-Perot resonator was introduced in Chapter 4. The design parameters such as

mirror reflectivity and the free spectral range dictate the resonator transmission properties.

In this context, the trade-offs encountered between the frequency modulation to intensity

modulation (FM-IM) sensitivity and the available detection bandwidth for the Fabry-Perot

resonator were identified. A mirror reflectivity of R = 60% was found to provide an ample

FM-IM sensitivity and an optimum optical detection bandwidth. The systematic measure-

ment uncertainty imposed on the time-resolved measurements due to frequency dependent

cavity life-time was described in detail. For a cavity length of 564µm cavity dispersion values

of +0.2 ps/GHz and −0.2 ps/GHz were calculated at the discrimination points of interest.

Excellent agreement was obtained between the predicted values and the experimental ones

with an error less than 1%. Subsequently in Chapter 5, the effect of cavity dispersion on

the measured time-resolved chirp was experimentally proved using a Lithium-Niobate based

Mach-Zehnder modulator. The calculated and measured chirping behavior were in excellent

agreement showing a smooth roll-off during the rise time of the pulse and a spike like be-

havior during the fall time of the pulse. To put in quantitative terms, the cavity dispersion

effects resulted in an underestimation of an assumed peak chirp of 6 GHz to 4 GHz during

the rise time of the optical pulse and slight overestimation of 6.1 GHz during the fall time of

the pulse. After gaining knowledge of the phase distortion of the Fabry-Perot resonator, one

can recalculate the time domain waveforms to eliminate the systematic measurement error.

Moreover, the effect of any random measurement uncertainty that might be introduced by

temperature fluctuations of the device under test (DUT) was presented. The corresponding

wavelength shift introduces an adiabatic shift of the measured time-resolved chirp profile.

These simple calculations illustrate that reliable time-resolved chirp measurements can be

112 Chapter 9. Conclusions

performed only if the device under test operates in a single stable longitudinal mode with

side mode suppression values of at least 25 dB. In Chapter 6, the designed time-resolved chirp

(TRC) measurement setup was successfully implemented for characterizing electroabsorption

modulated lasers emitting in the 1310 nm wavelength window at a data rate of 40 Gbps. A

peak to peak frequency chirp of about 7 GHz was extracted from the measurements after

calibrating the cavity dispersion effects. From the measured time-resolved chirp data an

effective chirp-parameter αH−eff of +0.43 was extracted, for a dynamic extinction of 9 dB at

1309 nm wavelength of operation. This very low chirp-parameter demonstrates the superior

performance of the electroabsorption modulated lasers over directly modulated lasers whose

chirp-parameter values have been reported to be as high as 7 [3,7], i.e., the chirping behavior

of the fabricated electroabsorption modulated lasers outperform by a factor of more than

15. Such low chirp-parameters enable longer transmission distances even at high data rates

reducing the link costs considerably. Unfortunately, due to insufficient side mode suppres-

sion ratio of the 1550 nm electroabsorption modulated lasers and 1550 nm electroabsorption

modulated lasers integrated with semiconductor optical amplifiers, time-resolved chirp in-

vestigations could not be performed. Nevertheless, physical mechanisms behind the chirping

behavior of electroabsorption modulated lasers have been investigated in detail with the use

of 1310 nm EMLs.

To summarize the salient features of the different methods employed for chirp investigations,

Kramers-Kronig transformations serve as a valuable tool in predicting the chirp-properties of

the material over the complete wavelength spectrum and aid in the design process of defin-

ing the operation wavelength of electroabsorption modulated lasers. Apart from material

and device properties, the dynamic frequency chirping behavior was illustrated to depend

on the driving electrical waveform. For instance, increasing the rise and fall times of the

modulating electrical waveform by a factor of two will increase the extent of frequency devi-

ation by a factor of two for non-zero values of modal refractive index changes or equivalently

non-zero chirp-parameter values. Thus time-resolved chirp investigations reveal the chirping

behavior of the device under realistic modulation conditions and after complete fabrication

of the device. This makes this method inevitable and more reliable for studying the chirping

properties of the fabricated structures. The small-signal chirp-parameter values for electroab-

sorption modulated lasers emitting in the 1310 nm wavelength window varied between +1.0

and −2.5 for EAM reverse bias voltages between 0 V and −2.5 V; i.e., the chirp-parameters

were strongly dependent on the applied EAM bias. In contrast, the dynamic chirping be-

havior was always positive over the complete modulation voltage swing between 0 V and

−2 V yielding an effective chirp-parameter of +0.43. Thus, the small-signal chirp-parameter

investigations are superfluous and are not mandatory for chirp investigations, since they do

not completely represent or predict the final dynamic frequency chirping behavior.

Using Kramers-Kronig transformations on the measured absorption spectra, it was deduced

that negative chirp-parameters for electroabsorption modulated lasers (EMLs) employing an

113

identical active area can only be realized for very low optical power levels; i.e., for insertion

losses in the range of 25–30 dB. Even electroabsorption modulated lasers employing individ-

ual optimization of the active layer or those employing hybrid approaches do not achieve high

optical power and negative chirp simultaneously due to the inherent larger wavelength de-

tuning exploited for their realizations. In order to achieve high optical power levels (without

external aids) and simultaneously realize low or negative chirp-parameters the integration of

a semiconductor optical amplifier with the electroabsorption modulated laser becomes indis-

pensable. The use of an identical active area makes the integration of such a semiconductor

optical amplifier straightforward without resorting to complicated fabrication technologies

which considerably increases the fabrication yield and reduces the final costs.

To demonstrate this potential, semiconductor optical amplifiers integrated with electroab-

sorption modulated lasers emitting in the 1550 nm wavelength window (1550 nm EML-SOAs)

were studied. The corresponding static and dynamic results were presented in Chapter 8.

Wide-open eye diagrams with a dynamic extinction of 9.8 dB and an average fiber-coupled

optical power of ≈ +0.6 dBm (1.15 mW) up to 40 Gbps were obtained for the first time, which

demonstrates the excellent high-speed performance of the integrated device. The bit error

rate performance (BER) of the 1550 nm EML-SOA was obtained at 10 Gbps by assuming

Gaussian distribution for the binary levels. Correspondingly, a BER of ≈ 8.5 × 10−12 was

extracted, excluding fiber dispersion and optical losses. The optical eye diagrams obtained

in all the measurements were limited by the driving electrical eye waveform which in part

degraded the obtained BER and extinction. Hence, the performance of the devices can be

treated as a lower bound. Low chirp-parameters were also obtained under small-signal condi-

tions for strong pumping of the laser. Although, large-signal chirping behavior could not be

performed, the small-signal chirp-parameter clearly decreased from +0.3 to −0.25 when the

laser current was increased from 40 mA to 140 mA at a constant bias voltage of −2 V on the

EAM. Thus, the reduction in the small-signal chirp is due to the increasing injected optical

power into the SOA section (which should not be confused with the decrease of the small-

signal chirp with applied bias voltage for the case of 1310 nm EMLs and 1550 nm EMLs).

This corroborates the effect of gain saturation effects leading to phase modulation in the

semiconductor optical amplifier for optical power levels of about 0 dBm (1 mW).

In Chapter 7, the large-signal modulation properties of electroabsorption modulated lasers

emitting in the 1550 nm wavelength window were studied experimentally with respect to

important device parameters such as laser current, EAM bias voltage and temperature. The

dynamic extinction and optical power levels were found to be strongly dependent on the

latter two parameters. For instance, the dynamic extinction ratio varied between 6 dB and

10 dB within a temperature interval of about 30C. In order to counteract the degradation

of the extinction ratio with temperature, the EAM bias voltage was actively controlled while

performing the measurements. This was accomplished by way of comprehensive temperature

dependent static measurements and subsequent extraction of the optimum bias voltages. The

114 Chapter 9. Conclusions

EAM bias was increased approximately by 0.3 V per 10C rise in temperature to guarantee

a temperature stable operation. A linear relationship between the EAM bias voltage and

temperature was found to be appropriate for an optimum performance with respect to power

and extinction ratio over a temperature range of 20C to 70C.

Thus for the first time, the feasibility of employing 1550 nm EMLs, employing an identical

active area based on the InGaAlAs/InP material system, operating over an extended tem-

perature range of 20C and 70C with excellent dynamic extinction ratios in the range of

8 dB to 10 dB for a voltage swing of 2.5Vpp up to 40 Gbps was demonstrated. A semi-cooled

operation of the EML was demonstrated to be viable by way of sensing the temperature and

simultaneously regulating the EAM bias voltage. Such semi-cooled operation saves on-chip

power consumption (required for temperature control within the mentioned range) up to

about 2.2 W. This is highly desirable for small form factor pluggable transceivers (e.g. XFP)

which typically operate at total power consumption levels less than 3.5 W.

To conclude, this work serves as a stepping-stone toward the deployment of electroabsorption

modulated lasers employing an identical active area for 40 Gbps systems employing direct

detection. They represent excellent candidates owing to their very low chirping behavior and

thereby reduced dispersion induced pulse broadening effects. Further motivations include

reduced fabrication costs, device compactness, and low drive voltage requirements besides

semi-cooled operation.

Appendix A

Device Layer Structure


# Function Material Thickness Bulk λPL Strain x y Doping ND

[nm] [µm] εxx [%] 1018/cm3

32 p-Contact GaxIn1−xAs 200 1.65 +0.6(t) 0.557 −2.0 (p)31 Cladding InP 1600 −0.5 (p)30 Grating 1 InP 45 −0.5 (p)29 Grating 2 GaxIn1−xAsyP1−y 130 1.05 0 0.137 0.301 −0.5 (p)28 Spacer InP 10 −0.5 (p)27 El.stopa AlxIn1−xAs 18 0.87 0 0.47 −0.5 (p)

26 SCH AlxGayIn1−x−yAs 80 1.05 0 0.315 0.15711×Barb AlxGayIn1−x−yAs 8 1.10 −0.5(tc) 0.265 0.27810×QW AlxGayIn1−x−yAs 5 1.29 +0.95(cd) 0.170 0.159

4 SCH AlxGayIn1−x−yAs 80 1.05 0 0.315 0.157

3 Spacer InP 1000 +1.0 (n)2 n-Contact GaxIn1−xAsyP1−y 200 1.2 0 0.25 0.55 +10 (n)1 Buffer InP 1000 +2.0 (n)

Substrate InP 360µm s.i.

aEl.stop = electron stopbBar = barrierct = tensiledc = compressive

Tab. A.1: Epitaxial layer structure for electroabsorption modulated lasers (EMLs) emitting inthe 1310 nm wavelength window. Nominal intrinsic layers have a n-type background doping of≈ 5 × 1016/cm3. The photoluminescence (PL) wavelength varies by approximately 40 nm across a2 inch wafer.

115

116 Appendix A. Device Layer Structure

1550 nm Electroabsorption modulated lasers&

1550 nm Electroabsorption modulated lasers integrated withsemiconductor optical amplifiers

# Function Material Thickness Bulk λPL Strain x y Doping ND

[nm] [µm] εxx [%] 1018/cm3

36 p-Contact GaxIn1−xAs 200 1.65 +0.6(t) 0.557 −2.0 (p)35 Cladding InP 1800 −0.5 (p)34 Grating 1 InP 45 −0.5 (p)33 Grating 2 GaxIn1−xAsyP1−y 100 1.05 0 0.137 0.301 −0.5 (p)32 Spacer InP 10 −0.6 (p)31 El.stopa AlxIn1−xAs 18 0 0.47 −0.5 (p)

30 SCH AlxGayIn1−x−yAs 30 1.05 0 0.315 0.1574×Barb AlxGayIn1−x−yAs 8 1.10 −0.5(tc) 0.265 0.2783×QW AlxGayIn1−x−yAs 5 1.54 +0.95(cd) 0.031 0.296

22 Spacer AlxGayIn1−x−yAs 30 1.109×Bar AlxGayIn1−x−yAs 8 1.10 −0.5(t) 0.265 0.2788×QW AlxGayIn1−x−yAs 7.5 1.51 +0.95(c) 0.073 0.255

4 SCH AlxGayIn1−x−yAs 30 1.05 0 0.315 0.157

3 Spacer InP 1000 +0.5 (n)2 n-Contact GaxIn1−xAsyP1−y 100 1.2 0 0.25 0.55 +10 (n)1 Buffer InP 1000 +2.3 (n)

Substrate InP 360µm s.i.

aEl.stop = electron stopbBar = barrierct = tensiledc = compressive

Tab. A.2: Epitaxial layer structure for electroabsorption modulated lasers (EMLs) emitting in the1550 nm wavelength window and electroabsorption modulated lasers integrated with semiconductoroptical amplifiers (EML-SOAs) emitting in the 1550 nm wavelength window. Nominal intrinsiclayers have a n-type background doping of ≈ 5×1016/cm3. The photoluminescence (PL) wavelengthvaries by approximately 40 nm across a 2 inch wafer.

Appendix B

Kramers-Kronig Relations

Consider a classical harmonic oscillator of mass m driven by an external force ~F. Let the

angular resonance frequency of the oscillator be ω0 and damping factor (e.g. frictional losses)

be given by γ. For reasonably small displacements x, the motion of the oscillator can be

described by a linear second-order differential equation of the form [2]

d2x

dt2+ γ

dx

dt+ ω2

0x =~F

m(B.1)

For an isolated atom in equilibrium, in the absence of any fields, the center of the nucleus

and the electron charge cloud coincide and the net electric dipole moment is zero. When

subject to a static electric field ~E, the light electron cloud is attracted toward the positive

terminal by a force ~F = q~E thereby resulting in a net dipole moment ~P = Neqxe, where

Ne is the number of electrons per unit volume, q the electronic charge, x the displacement

between the center of masses of the electron cloud and the nucleus and e the unit vector. A

schematic representation of the induced dipole moment is shown in Fig. B.1.

x

Center ofelectron cloud

Center of nucleusand electron cloud

Electron cloud

Center ofnucleus

Inducedpolarization P

External electric field E

Fig. B.1: Electric field induced distortion of electron cloud depicted for an isolated atom. Theresulting net dipole moment is directly proportional to the displacement of the center of masses ofthe electron cloud and the nucleus.

117

118 Appendix B. Kramers-Kronig Relations

Substituting for x and ~F in Eq. (B.1) and rearranging we obtain

d2~P

dt2+ γ

d~P

dt+ ω2

0~P =

Neq2~E

m0

(B.2)

By phenomenologically defining a material constant χ0 = Neq2/m0ǫ0ω0

2 comprising the

material properties with the electric permittivity of free space ǫ0 and the electron rest mass

m0, we can modify Eq. (B.2) as [2]

d2~P

dt2+ γ

d~P

dt+ ω2

0~P = ω2

0ǫ0χ0~E (B.3)

Eq. (B.3) gives the dynamic relation between the polarization density ~P and the electric field~E. Substituting a harmonic driving field of the form ~E(t) = ~E eiωt and equating coefficients

of eiωt after assuming a linear polarization response ~P(t) = ~Peiωt in Eq. (B.3), we obtain

(−ω2 + iγω + ω20)

~P = ω20ǫ0χ0

~E (B.4)

from which the polarization can be explicitly written as ~P = ǫ0 [χ0ω20/(ω

20 − ω2 + iγω)] ~E.

Writing the relation in the form ~P = ǫ0χ(ν)~E and substituting ω = 2πν we obtain an

expression for the frequency dependent susceptibility as

χ(ν) = χ0ν2

0

ν20 − ν2 + iν∆ν

(B.5)

where ν0 = ω0/2π is the resonance frequency and ∆ν = γ/2π. The real and imaginary parts

of χ(ν) are written as [2]

χ′(ν) = χ0ν2

0(ν20 − ν2)

(ν20 − ν2)2 + (ν∆ν)2

(B.6)

χ′′(ν) = −χ0ν2

0ν∆ν

(ν20 − ν2)2 + (ν∆ν)2

(B.7)

At frequencies well below resonance χ′(ν) ≈ χ0 and χ′′(ν) ≈ 0, so that χ0 is the low frequency

susceptibility. At frequencies well above resonance χ′(ν) ≈ χ′′(ν) ≈ χ0, the medium acts like

free space. At resonance ν = ν0, χ′(ν0) = 0 and −χ′′(ν) reaches its peak value of (ν0/∆ν)χ0.

A typical dielectric medium contains multiple resonances, corresponding to different lattice

and electronic vibrations. The overall susceptibility is the sum of the contributions from

all these resonances. Whereas the imaginary part of the susceptibility is confined near the

resonance frequency, real part contributes at all frequencies near and below resonance. Far

away from resonance, the refractive index is constant and the medium is nondispersive. The

real and imaginary parts of the complex susceptibility are related as follows [2]:

119

χ′(ν) =2

πP

∞∫

0

ν ′χ′′(ν ′)

ν ′2 − ν2dν ′ (B.8)

χ′′(ν) =2

πP

∞∫

0

νχ′(ν ′)

ν2 − ν ′2dν ′ (B.9)

Eqs. (B.8) and (B.9) form the Kramers-Kronig relations. The relations show that a knowledge

of the behavior of one of the quantities over the complete spectrum enables the determination

of the other. The symbol P stands for the Cauchy principal value of the integral defined as

P

∫

f(x, x′)dx′ ≡ lim∆→ 0

[∫ x−∆

−∞

f(x, x′)dx′ +

∫ +∞

x+∆

f(x, x′)dx′

]

, ∆ > 0 (B.10)

Physically, the Cauchy principal value evaluates the integral over the entire frequency range

excluding the singular point under consideration.

Appendix C

Frequency Domain Analysis

This appendix provides a concise introduction to the frequency domain analysis exploited

for illustrating the Fabry-Perot (FP) resonator dispersion effects (Sec. 4.3.4) and subsequent

calibration of the dispersion effects from the experimental time-resolved chirp measurements

(Sect. 5.2 and Sect. 6.4.2). A detailed description of the properties of Fourier transformation

and its applications to digital signal processing (DSP) can be found, for instance, in Refs.

[72,73].

time

S(t)

time

S (t)'

FS(t) F S ( )-1

'1 3

frequency

S( )S( )*H( )

frequency

S ( )'

2

C

C m- C m+

C m-2 C m+2

Fig. C.1: Sketch indicating the different steps involved in the frequency domain analysis of a timedomain signal. Schematic of the carrier frequency ωc and the side band frequencies spaced at amultiple of the modulation frequency ωm are shown.

A normalized time domain signal S(t) is Fourier transformed using a fast Fourier transform

(FFT) algorithm. Mathematically it is written as FS(t), where the operator ‘F’ stands for

Fourier transformation.

120

121

The resulting spectrum S(ω) in the frequency domain contains the amplitude and phase of

the individual spectral components that make up the time domain signal.

The effect of Fabry-Perot resonator on the time domain signal can be studied by imple-

menting a filter transfer function H(ω) which accounts for the FP transmission properties.

The transfer function H(ω), in general a complex function, consists of the magnitude re-

sponse |H(ω)| and the phase response arg[H(ω)] of the Fabry-Perot resonator as illustrated

in Fig. 4.12.

Convolving the two frequency domain signals, mathematically expressed as S(ω) ∗ H(ω),

where the operator ‘∗’ stands for the convolution operation, yields the modified frequency

domain signal S ′(ω). The resulting signal S ′(ω) is then inverse fast Fourier transformed

(IFFT) to reconstruct the time domain signal. Mathematically it is written as F−1S ′

(ω),where the operator ‘F−1’ stands for inverse Fourier transformation.

Calibrating Fabry-Perot dispersion

In this subsection, the calibration of Fabry-Perot cavity dispersion effects on the experimen-

tal time domain waveforms is described. In this case, we proceed from step 3 in Fig. C.1 to

step 1 since we want to nullify the dispersion effects of the FP transfer function.

As a first step, the time domain responses T+ and T− captured at an oscilloscope are Fourier

transformed individually. The resulting frequency spectra S′

+(ω) and S′

−(ω) are convolved in

two steps with the conjugate of the phase transfer function arg[H(ω)] by locking the carrier

frequency onto the discrimination points TD.

The so obtained S+(ω) and S−(ω) are then inverse Fourier transformed to obtain the time

domain waveforms without the dispersion effects. It should be noted that only the conjugate

of the phase transfer function is included in the calculations. The magnitude response |H(ω)|,in this case, will be set to ‘unity’ to let the wave pass through the Fabry-Perot resonator

without any change in amplitude. In other words, we implement a digital ‘all-pass’ filter

which forces the waveforms to retrace their path through the Fabry-Perot without modifying

the intensity of the waveforms but imposing a conjugated phase to calibrate the dispersion

effects.

Appendix D

List of Symbols

Roman

〈a〉 modal differential gain [m2]A Shockley-Reed-Hall recombination coefficient [1/s]AEAM area of an electroabsorption modulator contributing to capacitance [m2]B bimolecular recombination coefficient [m3/s]Bw bandwidth [Hz]BR bit rate [bits/s]c velocity of light in vacuum, 2.9979 × 108 [m/s]C Auger recombination coefficient [m6/s]CEAM capacitance of an electroabsorption modulator [F]CEAM,meas measured capacitance of an electroabsorption modulator [F]dpin intrinsic area thickness [m]dQW quantum well layer thickness [m]dT tunneling barrier thickness [m]Dλ dispersion coefficient or dispersion parameter [s/m2]e unit vectorE scalar electric field [V/m]E+ electric field amplitude of forward traveling wave [V/m]E− electric field amplitude of backward traveling wave [V/m]Ebar energy gap of barrier at 300 K [J]Ec carrier frequency amplitude [V/m]

(or) conduction band energy [J]Ec,offset ratio of conduction band offset to total band offset [J]Ee1 ground state electron energy [J]Eg bandgap energy at 300 K [J]Ehh1 ground state heavy hole energy [J]Eopt electric field strength of an optical wave [V/m]

Eopt complex amplitude of an optical wave [V/m]Ev valence band energy [J]EFc quasi-Fermi level for electrons [J]EFv quasi-Fermi level for holes [J]

122

123

E21 energy difference between states 2 and 1 [J]~E electric field strength [V/m]∆Ec conduction band offset [J]∆Ev valence band offset [J]∆EF separation of quasi-Fermi levels [J]f frequency [Hz]fm modulation frequency [Hz]fm,u frequency dips [Hz]f1 state 1 (valence band) Fermi occupation probabilityf2 state 2 (conduction band) Fermi occupation probabilityf3dBe modulation bandwidth [Hz]Fn amplifier noise figure~F force [N]F finesseF Fourier transform, mathematical operatorF−1 inverse Fourier transform, mathematical operatorg material power gain per unit length [1/m]〈g〉 modal power gain per unit length [1/m]〈dg〉 modal gain change [1/m]g0 peak gain coefficient [1/m]g(ω) gain coefficient frequency dependence [1/m]G(ω) amplification factorh Planck’s constant, 6.6262 × 10−34 [J·s]~ reduced Planck’s constant [J·s]H(ω) complex transfer functioni imaginary unit,

√−1

I current [A]I average current [A]Idet detected photocurrent [A]Ifm,det small-signal transfer function current [A]Iopt optical intensity [W/m2]IEAM photocurrent detected in an electroabsorption modulator [A]ILD laser pump current [A]ISOA semiconductor optical amplifier pump current [A]kB Boltzmann constant, 1.3807 × 10−23 [J/K]k0 propagation constant in vacuum [1/m]KFP Fabry-Perot resonator constantL lineshape functionL length [m]Lfiber fiber length [m]LDSF length of dispersion shifted fiber [m]LEAM length of electroabsorption modulator section [m]LFP cavity spacing of Fabry-Perot [m]LLD length of laser section [m]LSOA length of semiconductor optical amplifier section [m]

124 Appendix D. List of Symbols

∆LFP change in cavity spacing of Fabry-Perot [m]m small-signal intensity modulation index

(or) mass of a harmonic oscillator [kg]m0 rest mass of electron, 9.1095 × 10−31 [kg]m∗

r reduced effective mass of electron [kg]MT transition matrix elementn integern complex refractive indexn′ real part of complex refractive indexn′′ imaginary part of complex refractive index〈dn′〉 differential modal real refractive index change〈dn′′〉 differential modal imaginary refractive index changen′

clad cladding refractive indexn′

core core refractive indexn′

eff effective refractive index〈n′

eff〉 modal effective refractive indexn′

g group effective refractive indexn′

grat refractive index of grating materialn′

sub substrate refractive index∆n′ change in real part of refractive index∆n′′ change in imaginary part of refractive index∆n′

grat half peak to peak real refractive index variation defining the gratingN carrier density [1/m3]Ne number of electrons per unit volume [1/m3]Np photon density [1/m3]ND donor doping concentration [1/m3]p order of sideband

(or) integerp(n) probability of detecting n eventsP optical power [W]Pin input optical power [W]Pout output optical power [W]Psat saturation optical power [W]PON ON state optical power [W]POFF OFF state optical power [W]PN noise power [W]PS signal power [W]PIM average power due to intensity modulation [W]∆PFM power change due to frequency modulation [W]~P electric polarization density [C/m2]P principal value, mathematical operatorq elementary electron charge, 1.6022 × 10−19 [C]Q quality factorR mirror reflectivity of HR coated surface (≡ RHR)

(or) resistance [Ω]

125

Rsp spontaneous photon generation rate [1/m3 ·s]RAR mirror reflectivity of AR coated surfaceREAM series resistance of an electroabsorption modulator [Ω]RL load resistance [Ω]R responsivity [A/W]Si(f) power spectral density [W/(m2 ·Hz)]S(t) normalized time domain signalSEO small-signal electro-optic responseS11 small-signal electrical reflection coefficientS21 small-signal electrical transmission coefficientS(ω), S ′(ω) signal frequency spectrumS

′

+(ω), S′

−(ω) signal frequency spectrum

t time [s]T temperature [K]Tmax maximum transmissionTmin minimum transmissionTD discrimination point on a transmission responseTFP transmission of a Fabry-Perot resonatorT+ discrimination point where transmission increases with frequencyT− discrimination point where transmission decreases with frequencyu order of dipvg group velocity [m/s]V voltage [V]Vact active area volume [m3]Vbias voltage applied to a Mach-Zehnder modulator [V]Vpp peak to peak voltage [V]VEAM voltage applied to an electroabsorption modulator [V]Wridge width of ridge [m]x, y, z Cartesian coordinates [m]

(or) variablesX reactance [Ω]Z complex impedance [Ω]Z0 characteristic line impedance [Ω]

Greek

α material absorption per unit length [1/m]〈α〉 modal absorption per unit length [1/m]α0 residual absorption per unit length [1/m]〈α0〉 modal residual absorption per unit length [1/m]αi internal loss coefficient [1/m]αH chirp-parameter; also called Henry-parameter, alpha-parameterαH−eff effective chirp-parameterαH, signal additional chirp-parameter imposed by SOA

126 Appendix D. List of Symbols

αH, SOA chirp-parameter of SOA active materialβ propagation constant [1/m]βb Bragg propagation constant [1/m]βc carrier frequency propagation constant [1/m]βn n−th derivative of β with respect to ω [sn/m]βsp spontaneous emission factorβ1 first derivative of β with respect to ω [s/m]β2 second derivative of β with respect to ω [s2/m]β+1 first upper side band propagation constant [1/m]β−1 first lower side band propagation constant [1/m]γ damping factor [1/s]Γ confinement factor

(or) crystal orientationΓgrat grating confinement factorδb detuning from Bragg propagation constant [1/m]ǫ0 electric permittivity of free space, 8.8542 × 10−12 [F/m]ǫr relative dielectric permittivityǫxx biaxial strain in x-directionη quantum efficiencyηabs absorption efficiencyηc fiber coupling efficiencyηi internal quantum efficiencyκ coupling coefficient of a grating [1/m]λ wavelength in vacuum [m]λb Bragg wavelength [m]λin input wavelength [m]λmedium wavelength in a material medium [m]λDFB distributed feedback laser wavelength [m]λPL photoluminescence wavelength [m]λRF electrical wavelength [m]Λ grating period of a DFB laser [m]µ0 mean value of level ‘0’ (OFF state) [W]µ1 mean value of level ‘1’ (ON state) [W]ν frequency of light [Hz]νD frequency of light corresponding to the discrimination points [Hz]ν0 resonance frequency of an isolated atom [Hz]∆ν frequency change [Hz]

(or) spectral width [Hz]∆νg gain bandwidth [Hz]∆ν3 dB 3 dB optical bandwidth [Hz]π physical constant, 3.1416ρr reduced density of states [kg/(J2 ·s2 ·m)]σ0 standard deviation of level ‘0’ (OFF state) [W]σ1 standard deviation of level ‘1’ (ON state) [W]σ2

N,i noise current variance [A2]

127

σ2N, shot shot noise current variance [A2]

σ2N, thermal thermal noise current variance [A2]

τ carrier life-time [s]τp photon life-time [s]φ phase of the optical field [radians]Φ photon flux [photons/s]χ(ν) complex electric susceptibilityχ′(ν) real part of complex electric susceptibilityχ′′(ν) imaginary part of complex electric susceptibilityχ0 material constantω angular frequency of light [radians/second]ωc angular carrier frequency [radians/second]ωm angular modulation frequency [radians/second]ω0 angular resonance frequency of an isolated atom [radians/second]∆ω angular frequency deviation [radians/second]

Appendix E

List of Acronyms

1D one-dimensionAC alternating currentAM amplitude modulationAR anti-reflectionASE amplified spontaneous emissionBCB benzocyclobuteneBER bit error rateCB conduction bandCW continuous waveDC direct currentDCF dispersion compensating fiberDFB distributed feedbackDML directly modulated laserDOS density of statesDSF dispersion shifted fiberDSP digital signal processingDUT device under testEAM electroabsorption modulatorEDFA erbium-doped fiber amplifierEML electroabsorption modulated laserEML-SOA EML integrated with semiconductor optical amplifierE/O electro-opticFFT fast Fourier transformFM frequency modulationFM-IM frequency modulation to intensity modulationFP Fabry-PerotFSR free spectral rangeFWHM full width at half maximumGbps gigabit per secondGSG ground-signal-groundGVD group velocity dispersionHH heavy hole

128

List of Acronyms 129

HR high-reflectionIFFT inverse fast Fourier transformIM intensity modulationIR intermediate reachISI inter symbol interferenceITU international telecommunication unionLD laser diodeLEF linewidth enhancement factorL–I light–currentLR long reachMbps megabit per secondMOVPE metal organic vapor phase epitaxyMQW multiple quantum wellMZ Mach-ZehnderMZM Mach-Zehnder modulatorNRZ nonreturn to zeroPL photoluminescencePRBS pseudo-random binary sequenceQCSE quantum confined Stark effectQW quantum wellRC resistance-capacitanceRF radio frequencys.i. semi-insulatingSCH separate confinement heterostructureSDH synchronous digital hierarchySEM scanning electron microscopeSMF single-mode fiberSMSR side mode suppression ratioSNR signal to noise ratioSOA semiconductor optical amplifierSONET synchronous optical networksSPM self phase modulationSR short reachSRH Shockley-Reed-HallSSMF standard single-mode fiberTE transverse electricTEM transverse electro magneticTM transverse magneticTRC time-resolved chirpTWA traveling wave amplifierTWE traveling wave electrodeVB valence bandXFP 10 Gigabit small form factor pluggable

130

List of Publications

1. B. K. Saravanan, P. Gerlach, M. Peschke, T. Knoedl, R. Schreiner, C. Hanke, and

B. Stegmueller, “Integrated DFB laser electroabsorption modulator based on identical

MQW-double stack active layer for high-speed modulation beyond 10 Gbit/s,” in Proc.

IPRM’04, Kagoshima, Japan, May 31–Jun 4 2004, pp. 236–238.

2. B. K. Saravanan, C. Hanke, T. Knodl, M. Peschke, R. Macaluso, and B. Stegmuller,

“Integrated InGaAlAs/InP laser-modulator using an identical multiple quantum well

active layer,” in Proc. SPIE’05 Photonics West, Vol. 5729, San Jose, USA, Jan 22–27

2005, pp. 160–169.

3. B. K. Saravanan, T. Wenger, C. Hanke, P. Gerlach, M. Peschke and R. Macaluso, “Wide

temperature operation of 40-Gbps 1550-nm electroabsorption modulated lasers,” IEEE

Photon. Technol. Lett., vol. 18, no. 7, pp. 862–864, 2006.

4. M. Peschke, B. K. Saravanan, C. Hanke, T. Knoedl, and B. Stegmueller, “Investiga-

tion of the capacitance of integrated DFB-EAMs with shared active layer for 40 GHz

bandwidth,” in Proc. IEEE LEOS’04, Puerto Rico, USA, Nov 7–11 2004, pp. 673–674.

5. M. Peschke, P. Gerlach, B. K. Saravanan, and B. Stegmueller, “Thermal crosstalk

in integrated laser-modulators,” IEEE Photon. Technol. Lett., vol. 16, no. 11, pp.

2508–2510, 2004.

6. P. Gerlach, M. Peschke, C. Hanke, B. K. Saravanan, and R. Michalzik, “High-frequency

analysis of laser-integrated lumped electroabsorption modulators,” IEE Proc. Optoelec-

tronics, vol. 152, pp. 125–130, 2005.

7. P. Gerlach, M. Peschke, B. K. Saravanan, T. Knoedl, C. Hanke, B. Stegmueller, and

R. Michalzik, “40 Gbit/s operation of laser-integrated electroabsorption modulator us-

ing identical InGaAlAs quantum wells,” in Proc. IPRM’05, Glasgow, UK, May 8–12

2005.

8. P. Gerlach, M. Peschke, T. Knoedl, B. K. Saravanan, C. Hanke, B. Stegmueller, and

R. Michalzik, “Complex coupled distributed feedback laser monolithically integrated

with electroabsorption modulator at 1.3µm wavelength,” in Proc. CLEO Europe’05,

Munich, Germany, Jun 13–16 2005.

9. P. Gerlach, M. Peschke, T. Wenger, B. K. Saravanan, C. Hanke, and R. Michalzik,

“Complex coupled distributed feedback laser monolithically integrated with electroab-

sorption modulator and semiconductor optical amplifier at 1.3µm wavelength,” in Proc.

Photonics Europe’06, Strasbourg, France, Apr 2006 in press.

131

132 List of Publications

10. C. Hanke, B. K. Saravanan, T. Knoedl, M. Peschke, and B. Stegmueller, “Investigation

of the high-frequency performance of monolithic integrated laser-modulators,” in Proc.

SODC’04, Beijing, China, Mar 21–30 2004, pp. 63–66.

11. T. Knodl, C. Hanke, B. K. Saravanan, M. Peschke, R. Schreiner, and B. Stegmuller, “In-

tegrated 1.3µm InGaAlAs-InP laser–modulator with double-stack MQW layer struc-

ture,” in Proc. SPIE’04, Strasbourg, France, Apr 27–29 2004, pp. 1–7.

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Curriculum Vitae

19 Jan 79 Born in Mayiladuthurai, Tamil Nadu, India

Jun 82 – Apr 89 Auxilium Primary School, Thanjavur, India

Jun 89 – Apr 96 Kalyanasundaram Higher Secondary School, Thanjavur, India

Jun 96 – May 00 Bachelor of Engineering, B.E.Regional Engineering College, Tiruchirappalli, India

Aug 00 – Sep 00 German Language CourseGoethe Institute, Bremen, Germany

Oct 00 – Nov 02 Master of Science, M.Sc. in Materials ScienceTechnical University of Hamburg-Harburg, Germany

Jan 03 – Jan 06 Ph.D. workOptoelectronics Department, University of Ulm, Germany &Corporate Research, Infineon Technologies AG, Munich, Germany

Feb 06 – Mar 06 Dielectrics characterization for DRAM applicationsMemory Products, Infineon Technologies AG, Munich, Germany

since Apr 06 Applications Engineer, Electronic Manufacturing TestAgilent Technologies, Boblingen, Germany

Oct 01 – Dec 01 InternshipTransmission measurements in photonic crystal waveguidesCorporate Research, Infineon Technologies AG, Munich, Germany

Jan 02 – Mar 02 Student ProjectFDTD simulations of photonic crystal waveguides and Fabry-Perot filtersCorporate Research, Infineon Technologies AG, Munich, Germany

Apr 02 – Nov 02 Master ThesisChromatic dispersion measurements of photonic crystal waveguidesCorporate Research, Infineon Technologies AG, Munich, Germany

139

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Frequency Chirping Properties of Electroabsorption